# New risk quantifications

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## Recent papers

### Health and Portfolio Choices : a Diffidence Approach

with D. Crainich and L. Eeckhoudt
$E[u_1(w_{0}+\tilde{x},y) \tilde{x}] = 0 \Rightarrow E[u_1(w_{0}+\tilde{x},y+\tilde{\epsilon }) \tilde{x}] \leq 0$

The effect of health status on portfolio decisions has been extensively studied from an empirical viewpoint. In this paper, we propose a theoretical model of individuals’ choice of financial assets under bivariate utility functions depending on wealth and health. Our model relies on the diffidence theorem, which pertains to the class of hyperplane separation theorems. We establish the conditions under which the share of wealth held in risky assets falls as: 1) individuals’ health status deteriorates and; 2) individuals’ health status becomes risky. These conditions are shown to be related to the behaviour of the intensities of correlation aversion and of cross prudence as wealth increases.

European Journal of Operational Research

Vol. 259, N° 1, p. 273-279, 2017

### Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with the least-squares Monte Carlo method

with A. Floryszczak and M. Majri
$\hat{\text{NAV}}_{\phi(p)} = \frac{\sum\limits_{i=-M}^M \hat{\text{NAV}}_{\phi(p)+i}}{2M+1}$

The calculation of Net Asset Values and Solvency Capital Requirements in a Solvency 2 context – and the derivation of sensitivity analyses with respect to the main financial and actuarial risk drivers – is a complex procedure at the level of a real company, where it is illusory to be able to rely on closed-form formulas. The most general approach to perform- ing these computations is that of nested simulations. However, this method is also hardly realistic because of its huge computation resources demand. The least-squares Monte Carlo method has recently been suggested as a way to overcome these difficulties. The present paper confirms that using this method is indeed relevant for Solvency 2 computations at the level of a company.

Insurance: Mathematics and Economics

Vol. 71, p. 15-26, 2016