Jun
15
Wed
Second International Congress on Actuarial Science and Quantitative Finance
Jun 15 – Jun 18 all-day
Jun
16
Thu
Short Course: High-frequency statistics in Finance. Jean Jacod (UPMC-Paris 6) @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena
Jun 16 @ 8:00 am – 10:00 am

High-frequency statistics in Finance.
Jean Jacod (UPMC-Paris 6)

The aim of this course is to provide some basic facts about, and an overview of, statistics of processes which are observed at discrete times on a finite time interval. The domain of applications is primarily the study of observed stock prices.

After introducing the problem, we will explain which “parameters” of the model for the stock price or log-price can be identified, when it is observed at discrete times and when the frequency increases and eventually goes to infinity. The main parameters of this kind are the volatility and also the existence or not of jumps and their degree of activity when they are present. Then we will explain how it is possible to estimate these quantities, in a variety of settings (regular or irregular observation times, exact or noisy observation). If time permits, we will also mention some open Problems.

Short Course: Stochastic control for insurers; what can we learn from finance, and what are the differences?. Christian Hipp. @ Aula Máxima de Derecho. Claustro de San Agustín.
Jun 16 @ 8:00 am – 10:00 am

Stochastic control for insurers; what can we learn from finance, and what are the differences?.
Christian Hipp (Karlsruher Institute of Technology, Karlsruhe, Germany)

We give examples for stochastic control problems in insurance: optimal reinsurance (unlimited and limited excess of loss), optimal investment (without constraint: singularity, leverage, asymptotics), with constraints (no leverage, no shortselling and singularities caused by constraints), dividend optimisation and combinations. As methods for solution we discuss dynamic equations of Hamilton-Jacobi-Bellman type, the viscosity solution concept and a comparison argument for the insurance context. Emphasis is on numerical methods: we give an Euler type method which works in most cases and prove convergence.
Finally, we give a list of open problems together with heuristic solutions for a two objective problem: maximizing dividend payment under a ruin constraint.

Keywords: Stochastic Control, Viscosity Solutions, Euler type discretisations, Multi objective problem.

Coffee Break
Jun 16 @ 10:00 am – 10:30 am
Short Course: The New Post-crisis Landscape of Derivatives and Fixed Income Activity under Regulatory Constraints on Credit risk, Liquidity risk, and Counterparty risk. Nicole El Karoui, LPMA-UPMC @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena
Jun 16 @ 10:30 am – 12:30 pm

The New Post-crisis Landscape of Derivatives and Fixed Income Activity under Regulatory Constraints on Credit risk, Liquidity risk, and Counterparty risk.
Nicole El Karoui, LPMA-UPMC, Paris

Introduction
The motivation for this course is to update academic community on the deep transformation after the financial 2008- crisis in the world of interest rates, and credit derivatives induced by the regulation. Liquidity risk, credit risk, counterparty risk have become more bulky over the recent years, maybe than the market risk, given the identified lack of transparence in the OTC Market.

These risks can be mitigated by the way trade and post-trade functions are structured. At trading level, risks can be reduced by improving operational efficiency, e.g. ensuring electronic trade execution, affirmation and confirmation.This would have the effect of making OTC trade execution more similar to the way transactions are handled on-exchange.

One way is to impose collateral and margin requirements. In the bilateral clearing, the two counterparties most often have collateral agreements in place that provide for regular monitoring of how the value of the contract evolves so as to manage their respective credit exposures to each other. In the Central Counter-party (CCP)clearing, the CCP acts as a counterparty to each side of a transaction. It makes collateral management simpler, as it is the CCP that collects and manages collateral.

Special attention is dedicated to reduce credit risks notably in Credit Default Swap (CDS) market, since CDS are particularly vulnerable on many respects. The risk they cover-the credit risk- is not immediately observable but requires specific information about the borrower, which typically only banks have had. Assessing the risk remains difficult, and amplified by the fact that the potential obligations that come with them are extreme.

It is of crucial importance in a derivative business at a aggregated level, to (i) measure counterparty exposure, (ii) compute capital requirements, and (iii) hedge counterparty risk. Measuring counterparty exposure is important for setting limits on the amount of business a firm is prepared to do with a given counterparty; hedging it gives a possibility of mitigating it and transferring risk; and from a regulatory perspective there is significant pressure on financial institutions to have the capability of producing accurate risk measures to compute capital. In addition, computing counterparty exposure can also give insights into prices of complex products in potential future scenarios.The Risk Control, function attracting relatively limited attention in the past, is now becoming a central activity of all major financial institutions, requiring significant resources from all parties.

The aim of the course is to provide a bridge between old and new practices including counterparty risk in fixed income and credit derivatives market, first at the level of the bilateral contract, second at the aggregated level. In particular, we try to make a rigorous formulation of the different problems

Outline

First talk

The first part is dedicated to the basic foundations of the interest rates derivatives in a perfect market, by making a clear distinction between the different notions of funding, risk-free rate, bond, and also the notions of forward curve and discounting curve. As a consequence, we deduced the standard HJM framework
on interest rates dynamics and the notion of forward neutral probability measure. In regard, we describe the standard contracts as forward or future contracts, swaps, and the associated derivatives.

The second part is an (non standard) introduction of the default derivative world, where the basic contact is the CDS, without specific mathematical tools. Default spreads and other similar quantities appear naturally. A general framework is then introduced. Examples of affine models. These tools are necessary to model the liquidity risk in the interbank market, and the multi-discounting curves. Different examples are developed.

Second talk

Pricing with collateral: some typical non-linear backward stochastic equation for pricing. Right-way/Wrong-way risk;

Hedging and Managing counterparty risk; aggregation and risk mitigation; stress testing.

Bibliography

Cesari, G., Aquilina, J., Charpillon, N., Filipovic, Z., Lee, G., & Manda, I. (2009). Modelling, pricing, and hedging counterparty credit exposure: A technical guide. Springer Science & Business Media.

Grbac, Z., & Runggaldier, W. J. (2015). Interest Rate Modeling: Post-Crisis Challenges and Approaches.

Henrard, M. (2013). Multi-curves framework with stochastic spread: A coherent approach to STIR futures and their options. OpenGamma Quantitative Research, (11).

Short Course: Using Bayesian MCMC Models for Stochastic Loss Reserving. Glenn Meyers. ISO Innovative Analytics @ Aula Máxima de Derecho. Claustro de San Agustín.
Jun 16 @ 10:30 am – 12:30 pm

Short Course: Using Bayesian MCMC Models for Stochastic Loss Reserving.
Glenn Meyers. ISO Innovative Analytics.

The course will open with an explanation of Bayesian MCMC models and the software used to implement these models. It will then walk through some of the details of the models discussed in the plenary talk. These will include:
The Correlated Chain Ladder (CCL) model for incurred loss triangles
The Changing Settlement Rate (CSR) model for paid loss triangles
A bivariate model for stochastic loss reserving of two lines of insurance
Using a Bayesian MCMC model to calculate cost of capital risk margins
The scripts that implement these models are written in the R programming language using the rstan package for Bayesian MCMC modeling. These scripts will be made available to course attendees upon request.

Keywords:Bayesian MCMC, Stochastic Loss Reserving, Dependencies, Risk Margins, Schedule P, R Programming Language, rstan

References
Meyers, Glenn G. 2015. “Stochastic Loss Reserving Using Bayesian MCMC Models” CAS Monograph Series, No. 1.
Meyers, Glenn G. 2016. “Dependencies in Stochastic Loss Reserve Models” Casualty Actuarial Society Forum (Winter)

Plenary Talk: Mitigating Extreme Risks Through Securitization. Qihe Tang. University of Iowa, USA @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 16 @ 2:00 pm – 3:00 pm

Mitigating Extreme Risks Through Securitization
Qihe Tang.
University of Iowa, USA

Recent decades have seen an unprecedented surge in the frequency and severity of catastrophes, be they natural (such as earthquakes, floods, droughts, hurricanes, tsunamis, and wildfires) or man-made (such as terrorist attacks, financial crises, and wars), all of which wrought havoc on the environment, economy, and society on a large scale despite their low likelihood of happening. This has caught much attention from academics, practitioners, and regulators. In particular, various Insurance-Linked Securities (ILS) as risk transfer mechanisms have been devised in this general trend, in addition to traditional reinsurance, to help insurers and reinsurers transfer catastrophe risks to the capital market. So far, the most successful ILS in the market are Catastrophe (CAT) bonds and Industry Loss Warranties (ILWs). In this talk we shall discuss issues of pricing CAT bonds and quantifying the basis risk of ILWs. To tackle these issues, we shall mainly employ techniques from Extreme Value Theory (EVT).

This talk is based on several recent joint works with Zhongyi Yuan at the Pennsylvania State University.

Plenary Talk: Stochastic control for insurance: new problems and methods. Christian Hipp (Karlsruher Institute of Technology, Karlsruhe, Germany) @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 16 @ 3:00 pm – 4:00 pm

Plenary Talk: Stochastic control for insurance: new problems and methods. Christian Hipp (Karlsruher Institute of Technology, Karlsruhe, Germany)

Stochastic control for insurance is concerned with problems in insurance models (jump processes) and for insurance applications (constraints from supervision and market). This leads to questions of the following type:
1. How to find numerically a viscosity solution to an integro differential equation;
2. Uniqueness of viscosity solutions when boundary conditions are values of derivatives; and
3. How to solve control problems with hidden variables.
We shall present simple Euler schemes (similar to the ones in Fleming-Soner (2006), Ch. IX) which converge when the value function has a continuous first derivative. This Euler discretisation works in many univariate control problems also when value functions are without continuous second (and first!) derivative. Cases with non smooth value function arise when claim size distributions are atomic or when constraints are restrictive.
Examples for control propblems with hidden variables are a) Bayesian models or mixture models in which the mixing variable is not observable, and these cases are usually solved with a filter approach. Or b) multi-objective problems with an objective function with dimension 2 or larger. The most studied problem of type b) is mean-variance optimisation with finite horizon in portfolio management. We shall consider an infinite horizon problem: maximize dividend payment and minimize ruin probability. This problem will be described and partly solved in three simple models: in the (time and space discrete) de Finetti model, in the classical Lundberg model with exponential claims, and in a simple diffusion model. The dynamic equations for these problems are (almost) hopeless. Instead, heuristic methods are proposed which lead to suboptimal solutions not too far from optimal solutions, and which speed up policy improvement algorithms.

Coffee Break
Jun 16 @ 4:00 pm – 4:30 pm
Poster Session @ Sala de Exposiciones. Piso 1. Casa Museo Arte y Cultura la Presentación.
Jun 16 @ 4:30 pm – 5:30 pm

Poster Session

Short Term American Path Dependent Option Pricing in the USDCOP Market: Central Bank’s Volatility Control Option Case
Santiago Stozitzky*, Bancolombia

A stochastic approach to pricing financial instruments for the Caribbean markets
Stephen Barnes*, University of the West Indies; Conall Kelly, University of the West Indies; Alexandra Rodkina, University of the West Indies

Estimating and Forecasting the Term Structure of Interest Rates:US and Colombia Analysis
Cristhian Rodriguez*, Urosario

Modeling the Uruguayan Sovereign Debt
Andrés Sosa*, Centro de Matemática, UdelaR

Nonlinear options pricing and Feynman Kac’s theorem
John Moreno*, U. Externado de Colombia

Extreme returns in the mining gold stock and in gold prices
Gonzalo Ubal*, Universidad de Talca

Modeling and Forecasting of the Relationship between Airline Stocks and Oil Market
Erik Muñoz*, Universidad de Talca

Neural networks in sovereign rating: application to Colombia, period between 1838-1900
Mauricio Avellaneda Hortua*, Universidad Externado de Colombia

El modelo Lee-Carter para estimar y pronosticar mortalidad: Una aplicación para Colombia
Carlos Ochoa*, Universidad Nacional

NUMERICAL APPROXIMATION OF VEGA UNDER THE STOCHASTIC VOLATILITY MODEL OF HERSTON, USING THE PATHWISE-EULER METHOD
Ana Maria Serrato Polania*, Universidad Externado

Synthetic portfolio for event studies: Estimating the effects of volatility call auctions
Diego Agudelo, Universidad EAFIT; Carlos Castro Universidad del Rosario; Sergio Preciado*, Universidad del Rosario

Contributed Talks 3: Academic–Actuarial Science–Property-Casualty, General Insurance, Non-Life**.
Jun 16 @ 5:30 pm – 7:00 pm

5:30pm–6:00pm
Classical Reserving – Double Chain Ladder and its Extensions
Carolin Margraf*, Cass Business School, London; Jens Nielsen, Cass Business School, London; Maria Martinez Miranda, University of Granada, Spain; Munir Hiabu, Cass Business School, London
In this paper, we propose different methods based on the Double Chain Ladder (DCL) framework introduced by Martinez-Miranda, Nielsen, and Verrall (2012a). The aim of reserving in non-life insurance is to forecast the amount of claims which have been underwritten in the past, but are not settled yet. For as long as anyone remembers, non-life insurance companies have used the so called chain ladder method to reserve for outstanding liabilities. In the DCL framework, we build on this classical reserving method and also add the information of reported counts data to the classical reserving data. By using more data, it is expected that the method will have less volatility than the celebrated chain ladder method.
Not only do we derive a surprisingly simple method for forecasting the outstanding liabilities but we are also able to estimate RBNS (reported but not settled) and IBNR (incurred but not reported yet) claims separately. Furthermore, we benefit from the advantages of having a full stochastic cash flow model of outstanding liabilities for the model developed in Verrall, Nielsen and Jessen (2010).This way, we can take advantage of the simple relationship between development factors which allows us to involve and then estimate the reporting and payment delay.
In this work, we investigate the Double Chain Ladder model further and consider the case when other knowledge is available, namely prior knowledge or expert knowledge. Initially we focus on prior knowledge on the number of zero-claims for each underwriting year and prior knowledge about the relationship between the development of the claim and its mean severity. Both types of prior knowledge readily lend themselves to be included in the DCL framework. Furthermore, we want to include a mixture of paid data and expert knowledge, incurred data, in different ways. More precisely, we use incurred data to rectify one weak point for DCL and CLM where the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. In addition, we take advantage of this expert knowledge and use it as an estimate for the RBNS claims. We include an empirical illustration that illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method.
This paper constructs for the first time a full statistical cash flow model of the incurred chain ladder method useful for asset-liability hedging, capital allocation and other management decision tools.
We also apply bootstrap estimation to approximate the predictive distributions. This is an alternative to the widely used England and Verrall (1999) bootstrap which might have to restrictive assumptions.

6:00pm–6:30pm:
Risk Measure Preserving Piecewise Linear Approximation of Empirical Distributions
William Guevara Alarcón*, Université de Lausanne; Philipp Arbenz, SCOR.
Stochastic models used for pricing, reserving, or capital modelling in insurance companies are often very complex, which is why resulting distributions are typically approximated by Monte Carlo simulations. Both the market and regulators exert increasing pressure not to discard the resulting sample distributions, but rather to store them for future review, audit, or validation, as well as to transfer them between actuarial systems. The present work introduces a compression algorithm which approximates an empirical univariate distribution function through a piecewise linear distribution. In contrast to keeping the full sample, such an approximation facilitates the storage and data transfer of the results by drastically reducing memory requirements. The approximation algorithm preserves the mean and imposes a uniformly bounded relative error over a space of coherent risk measures (TVaR). An efficient, open source implementation is provided.

6:30pm–7:00pm:
In-sample forecasting with local linear survival densities – A continuous chain ladder approach
Munir Hiabu*, Cass Business School; Maria Martinez Miranda, University of Granada, Spain; Enno Mammen, ; Jens Nielsen, Cass Business School, London
Non-life insurance companies mostly use the so called chain ladder method for reserving outstanding liabilities.
Chain ladder and all its extensions are based on aggregated run-off triangles. In this talk we will show how to translate the chain ladder method into a continuous framework using granular data. In contrast to the few granular methods which already exist, we will keep the basic structure of having observations on a triangle. As it turns out, chain ladder, and thus also our continuous analogue, is an in-sample technique where no extrapolation is needed to forecast the reserve. The in-sample area is defined as one triangle (the “upper triangle”) and the forecasting area as the second triangle (the “lower triangle”) that added to the first triangle produces a square. We call our approach in-sample forecasting. The in-sample forecasting will be performed with non-parametric methods in a survival analysis framework. In the first part of the talk we will focus on the multiplicative density structure which also is the underlying assumption of chain ladder. Calendar and seasonal effects do not follow this multiplicativity assumption. Therefore, in the second part of the talk, we will show how to go beyond this multiplicativity assumption in order to get more accurate forecasts. A real data example and a simulation study will be provided to support the theory.

Contributed Talks 4: Academic–Finance–Other**. @ Casa Museo Arte y Cultura la Presentación.
Jun 16 @ 5:30 pm – 7:00 pm

5:30pm–6:00pm:
Calibration in Option Pricing with Forward and Backward Reduced Models
Jose Silva*, University of Wuppertal; E. Jan ter Maten, University of Wuppertal; Michael Guenther, University of Wuppertal
This work presents the calibration of a stochastic volatility model, the Heston Model using Model Order Reduction. The calibration within the context of financial markets usually goes along the following lines. After defining which model or models suit the behaviour of each market the best, e.g. FX Markets, Stock Markets, etc., the information regarding currently priced instruments in the market is gathered. Using simple, quick models one obtains an estimate of at which value of the parameters is the market currently trading. These estimates are posteriorly used to priced more complexed or exotic products.
A very common calibration process involves a least-squares minimization problem in which each cost function evaluation involves solving one partial differential equation (PDE) per each set of parameters available on the market. This can quickly become prohibitively expensive to solve numerically. For that reason two parallel strategies are presented in this work, which should improve considerably the cost of such calibrations.
Obtaining a Dupire-type equation for both models, we proceed to calibrate option prices to market data by a least-squares minimization. We present the results showing the computational efficiency and comparing it with the ones resulting from a parametric reduced order model. We use Alternating-Direction Implicit schemes to numerically solve the partial differential equations in both approaches.

6:00pm–6:30pm:
Prediction of Federal Funds Target Rate: A Dynamic Logistic Bayesian Model Average Approach
Hernán Alzate*, Bancolombia S.A.; Andrés Ramírez-Hassan, EAFIT University
In this paper we examine which macroeconomic and financial variables have most predictive power for the target repo rate decisions made by the Federal Reserve. We conduct the analysis for the FOMC decisions during the period June 1998-April 2015 using dynamic logistic models with dynamic Bayesian Model Averaging that allows to perform predictions in real-time with great flexibility. The computational burden of the algorithm is reduced by adapting a Markov Chain Monte Carlo Model Composition: MC3. We found that the outcome of the FOMC meetings during the sample period are predicted well: Logistic DMA-Up and Dynamic Logit-Up models present hit ratios of 87,2 and 88,7; meanwhile, hit ratios for the Logistic DMA-Down and Dynamic Logit-Down models are 79,8 and 68,0, respectively.

6:30pm–7:00pm:
Stochastic Portfolio Theory: A Machine Learning Perspective
Alexander Vervuurt*, University of Oxford; Yves-Laurent Kom Samo, University of Oxford
We propose a novel application of Gaussian processes to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework recently introduced by Robert E. Fernholz that aims at flexibly analyzing the performance of certain investment strategies in stock markets relative to benchmark indices. In particular, SPT has exhibited some investment strategies based on company sizes that, under realistic assumptions, outperform benchmark indices with probability 1 over certain time horizons. Galvanized by this result, we consider the inverse problem that consists of learning (from historical data) an optimal investment strategy based on any given set of trading characteristics, and using a user-specified optimality criterion that may go beyond the outperformance of a benchmark index. Although the inverse problem is of the utmost interest to investment management practitioners, it can hardly be tackled using the SPT framework. We show that our machine learning approach learns investment strategies that considerably outperform existing SPT strategies in the US stock market.

Invited Session–Philip Protter @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 16 @ 5:30 pm – 7:00 pm

5:30pm–6:00pm
Some remarks on functionally generated portfolios
Johannes Ruf*, UCL; Ioannis Karatzas, Columbia
In the first part of the talk I will review Bob Fernholz’ theory of functionally generated portfolios. In the second part I will discuss questions related to the existence of short-term arbitrage opportunities. This is joint work with Ioannis Karatzas

6:00pm-6:30pm
Martingale Optimal Transport and Beyond
Marcel Nutz*, Columbia
We study the Monge–Kantorovich transport between two probability measures, where the transport plans are subject to a probabilistic constraint. For instance, in the martingale optimal transport problem, the transports are laws of martingales. Interesting new couplings emerge as optimizers in such problems.
Constrained transport arises in the context of robust hedging in mathematical finance via linear programming duality. We formulate a complete duality theory for general performance functions, including the existence of optimal hedges. This duality leads to an analytic monotonicity principle which describes the geometry of optimal transports. Joint work with Mathias Beiglböck, Florian Stebegg and Nizar Touzi.

6:30pm–7:00pm
Dynamic Programming Approach to Principal-Agent Problems
Dylan Possamaï*, Université Paris Dauphine; Nizar Touzi, Ecole Polytechnique; Jaksa Cvitanic, Caltech
We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon. Our approach is the following: we first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation and for which the agent’s optimal effort is straightforward to find. We then show that, under technical conditions, the optimization over the restricted family of contracts represents no loss of generality. Moreover, the principal’s problem can then be analyzed by the standard tools of control theory. Our proofs rely on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.

Jun
17
Fri
Plenary Talk: Path-Dependent Volatility. Julien Guyon. Bloomberg LP. New York, US @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena
Jun 17 @ 8:00 am – 9:00 am

Path-Dependent Volatility
Julien Guyon
Bloomberg LP. New York, US

So far, path-dependent volatility models have drawn little attention from both practitioners and academics compared to local volatility and stochastic volatility models. This is unfair: in this talk we show that they combine benefits from both. Like the local volatility model, they are complete and can fit exactly the market smile; like stochastic volatility models, they can produce rich implied volatility dynamics. Not only that: given their huge flexibility, they can actually generate a much broader range of spot-vol dynamics, thus possibly preventing large mispricings, and they can also capture prominent historical patterns of volatility. We give many examples to showcase their capabilities.

Plenary talk: Aggressive Backtesting of Stochastic Loss Reserve Models – Where It Leads Us. Glenn Meyers, ISO Innovative Analytics, New York USA. @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 17 @ 9:00 am – 10:00 am

Aggressive Backtesting of Stochastic Loss Reserve Models – Where It Leads Us
Glenn Meyers
ISO Innovative Analytics,
New York USA.

In 2012 the was posted on the Casualty Actuarial Society website. This database includes several hundred loss triangles compiled from the American Schedule P exhibits that are reported to the American National Association of Insurance Commissioners. The database includes subsequent outcomes that were reported after the original loss triangle was reported.
Since the database was compiled, the speaker has used this database test the predictions of two currently popular stochastic loss reserve models and found some shortcomings of these models. The talk will discuss new models that are fit with Bayesian MCMC algorithms that address these shortcomings. The talk will then go on to show how these models can be used to address the current problems of dependencies between lines of insurance, and cost of capital risk margins.

Keywords: Bayesian MCMC, Stochastic Loss Reserving, Dependencies, Risk Margins, Schedule P

Coffee Break
Jun 17 @ 10:00 am – 10:30 am
Contributed talks 5: Practitioner–Finance** (English, Spanish) @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 17 @ 10:30 am – 12:00 pm

10:30am–11:00am:
A systematic view on price based trading strategies
A. Christian Da Silva*, Dunn Capital; Fernando Ferreira, USP; Ju-Yi Yen, University of Cincinnati
We study trading strategies that use historical price data to predict future asset performance. Important and well known examples are short-term or long-term reversal cite{Bondt1989}, momentum and trend-following cite{JT1993,BP}. A distinction between these strategies is the extension of historical data used to predict the future. In particular, short-term reversal appears for portfolios which are build using historical data up to one month. Trend-following and momentum are generally implemented using few months to one year and long-term reversal uses few years of historical data.
We study such strategies by assuming that the asset log-returns $x_{i}$ are Gaussian random variables with drift $mu$, variance $V$ and autocorrelation $rho$ cite{FSY}. We further assume to be able to trade proportional to a simple moving average ($m(T)$) with $T$ terms and calculate the exact expression for the average performance and its variance cite{FSY}.
Empirically we identify the different regimes (from short-term reversal to long-term reversal and beyond) by presenting the Sharpe ratio of our strategy applied to 120 years of the DJIA as a function of $T$.

11:00am–11:30am (Spanish):
An Application of Extreme Value Theory for Measuring Financial Risk in the Uruguayan Pension Fund
Guillermo Magnou*, SURA
Traditional methods for financial risk measures adopts normal distributions as a pattern of the financial return behavior. Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. In this paper, we use Peaks Over Threshold (POT) model of Extreme Value Theory (EVT), and General Pareto Distribution (GPD) which can give a more accurate description on tail distribution of financial losses. The EVT and POT techniques provides well established statistical models for the computation of extreme risk measures like the Return Level, Value at Risk and Expected Shortfall. In this paper we apply this technique to a series of daily losses of AFAP SURA over an 18-year period (1997-2015), AFAP SURA is the second largest pension fund in Uruguay with more than 310,000 clients and assets under management over USD 2 billion.
Our major conclusion is that the POT model can be useful for assessing the size of extreme events. VaR approaches based on the assumption of normal distribution are definitely overestimating low percentiles (due to the high variance estimation), and underestimate high percentiles (due to heavy tails). The absence of extreme values in the assumption of normal distribution underestimate the Expected Shortfall estimation for high percentiles. Instead, the extreme value approach on POT model seems coherent with respect to the actual losses observed and is easy to implement.

11:30am–12:00am (Spanish):
Empirical Approach to the Heston Model Parameters on the Exchange Rate USD / COP
Carlos Grajales*, Universidad de Antioquia; Santiago Medina, Universidad Nacional de Colombia
This work proposes an empirical calibration of the Heston stochastic volatility model for the exchange rate USD / COP. The parameter estimation is done by developing an algorithm that performs simulated trajectories for the exchange rate under
Heston model and looking for matching probability distributionof simulated paths with the probability distribution that comes from the real exchange rate. The calibration is achieved by using both two-sample KS test and Nelder Mead simplex direct search. At the end, the results show that although achieving multiple optima parameter values depending on an initial vector parameter is posible, one of these could be chosen according to financial market information. The ongoing suggested open problems that come with the underlying dynamics presented will be related with
derivatives and risk measures valuation

Contributed talks 6: Practitioner–Actuarial Science** & Academic–Actuarial Science–Education** (English, Spanish) @ Aula Máxima de Derecho. Claustro de San Agustín.
Jun 17 @ 10:30 am – 12:00 pm

10:30am–11:00am:
Value-at-Risk Estimation of Aggregated Risks Using Marginal Laws and Some Dependence Information
ANDRES CUBEROS ACEVEDO*, SCOR; Esterina Masiello, Univ Lyon, Institut Camille Jordan,; Veronique Maume-Deschamps, Univ Lyon, Institut Camille Jordan,
Estimating the Value-at-Risk of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment… This question has been widely treated but new efficient methods are always welcome; especially if they apply in (relatively) high dimension. We propose an estimation procedure based on the checkerboard approximation of the empirical copulas. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard approximation some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples.

11:00am–11:30a.m.:
Basel and Solvency: Brazilian Experience
ELIZABETH BORELLI*, PUCSP; FABIANA SILVA, PUCSP; VIVIAN CANOAS, PUCSP
This article aims to discuss the instruments related to the economic stability and solvency of financial institutions such as banks, insurers and reinsurers, with regards to the guaranteed assets and rights of investors and insureds as well as its financial impact on the Brazilian market. The analysis assumes that the capital requirement constitutes the most important and powerful protection tool for financial institutions against the risk of insolvency, with the purpose that pacts like Basel and Solvency are intended to form reserves capable of supporting fluctuations against inherent risks to the activities they perform, as mechanisms for absorbing variations against unexpected losses. In this context, it is briefly presented the history of these agreements in the world, followed by the analysis of its implementation and impact in Brazil, where regulators have also created procedures to suit the market, by adapting the legislation for banks, insurers and reinsurers and new capital requirements. It is concluded that this process of evolution and regulation must constantly be monitored so that new conditions can be incorporated in the models, to ensure the solvency of the market. It was found that profitability values and ratios for banks have been reduced due to the higher capital requirements and consequent reduction in financial leverage ratios to these companies after the implementation of Basel I and Basel II projects in Brazil. In the insurance market, the higher capital requirements penalized smaller companies, which can reduce competitiveness. However, despite the unfavorable financial impact in some measure, it is important to consider the positive effect of greater stability to the system.

11:30am–12:00m (Spanish):
On four documents by Julio Garavito on actuarial mathematics and insuraces
Fabio Ortiz*, U. Externado-U de los Andes
We present four documents by te colombian engineer Julio Gravito (1865-1920) in which he dealt with topics in actuarial mathematics and insurances.
Julio Garavito was a professor at Universidad Nacional de Colombia from around 1895 to 1920 . His interest in several fields of pure and applied mathematics and his self cultivated scientifical interest made of this engineer one the few professors who published articles on several subjects.
One of this was he interst in actuarial mathematics and insurances. We will comment on four articles on this field and actuarial mathematics, three of which are unpublished:
Calculation of premiums and reserves of life insurances made for the Sociedad Nacional de Seguros (1902-1903): in this document he
uses the text of E. Dormoy (Doroy (1878)) to explain the theory of calculation of policies different premiumms and he explains the use of a mortality table for which purpose he uses tables from United States and England. Altough the document was made for the calculation of the insurance conpany and is unpublished, a description of this and some commentes was made in Ortiz(2014)
The second document Notes on the insurances companies is an unpublished exposition on actuarial mathematics in which he explains the calculation of premiums and reserves on one or two heads. Accordig to the used notation the exposition is based on Dormoy (1878).
The third one is Seguro Agricola published in 1931 altough it was presented to the Agricultural Congress in 1911. In this exposition explains the adventages of promoting agricole assurances and policies for the reinforcement of this economical activity in Colombia.
The fourth document is Compania Cooperativa de Constructores. In this document he deals with a cooperative associaion in which a number of members can get the ownership of one house in such a manner that the cooperative has the mortage and the houses are alloted to a grou pf members by sweepstakes. The problem is to calculate the number of members supposed to get loans for the houses to be alloted during a number of periods so that the cooperatve association can hold all the mortage

SOCIEDAD LATINOAMERICANA DE ACTUARÍA Y FINANZAS @ Auditorio Paraninfo. Claustro San Agustín. Universidad de Cartagena.
Jun 17 @ 12:00 pm – 12:30 pm

SOCIEDAD LATINOAMERICANA DE FINANZAS CUANTITATIVAS Y CIENCIAS ACTUARIALES
Comité Organizador ICASQF

Se invita a la presentación de la sociedad Latinoamericana de Finanzas Cuantitativas y Ciencias Actuariales Se hará una breve descripción de los objetivos, misión y alcance de la sociedad. La invitación es abierta a todos los estudiantes, profesionales, investigadores y educadores que están interesados en el fortalecimiento académico del modelamiento cuantitativo de Finanzas y Actuaría en Latinoamérica.

Tour in Chiva
Jun 17 @ 2:00 pm – 6:00 pm

Traditional “Chiva” bus tour: Bocagrande, Cartagena Bay, Monument of the Old Shoes, “La Popa” Monastery, San Felipe Castle –entrance included-, old vaults. . Open to all registered participants (no extra fee), confirmation is compulsory.

The meeting point is at 2:30pm at the old vaults “Las Bovedas Artesanales” There are limited places available, so please return a form included in the registration package to the registration desk as soon as possible. Forms will only be received until 5:00 pm on the first day of the conference (Wednesday June 15, 2016).