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.
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.
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