Short Course: Stochastic control for insurers; what can we learn from finance, and what are the differences?. Christian Hipp.

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.

Short Course: TUTORIAL ON STOCHASTIC PORTFOLIO THEORY. IOANNIS KARATZAS

TUTORIAL ON STOCHASTIC PORTFOLIO THEORY.
IOANNIS KARATZAS
(Columbia University and INTECH Investment Management LLC)

The goal of this series of four one-hour lectures is to introduce Stochastic Portfolio Theory, a rich and flexible framework for analyzing portfolio behavior and equity market structure, and to explore some of its applications to portfolio management and performance measurement.
The first three lectures are intended for a general audience; very little background is assumed.The third lecture will be of particular interest to portfolio managers who wish to learn of new methods of measuring the impact of size on their equity portfolios. The last lecture is designed for a more mathematically advanced audience, although all relevant background materialwill be I ntroduced throughout.
Here is a detailed summary of the four one-hour lectures:
Lecture 1: The Model for a Stock PriceLogarithms; basic probability theory, random variables, mean and variance; random walks; Brownian motion; drift; stock price models; rates of return and growth rates.
Lecture 2: Introduction to Stochastic Portfolio TheoryMultiple stocks; portfolio rate of return and growth rate; Excess Growth Rate (EGR); relative growth rates and numeraire independence of EGR; the EGR of the market portfolio.
Lecture 3: Size and the Distribution of CapitalStability of markets; the size effe ct; market diversity and diversity-weighted portfolios; the distributional component of return.
Lecture 4: The Mathematics of Stochastic Portfolio TheoryDefinitions; why the EGR of an all-long portfolio is nonnegative; portfolio generating functions; diversity and relative arbitrage; local times and ranked generating functions.

References:

E.R. FERNHOLZ (2002) Stochastic Portfo
lio Theory. Springer Verlag, NY.

E.R. FERNHOLZ & I. KARATZAS (2009) Stochastic Portfolio Theory: An Overview.
Handbook of Numerical Analysis XV (A. Bensoussan & Q. Zhang, Editors). North-Holland, Amsterdam and Boston.

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

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.

SOCIEDAD LATINOAMERICANA DE ACTUARÍA Y FINANZAS

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.

Short Course: Stochastic control for insurers; what can we learn from finance, and what are the differences?. Christian Hipp.

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.

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

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: 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

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).