# New risk quantifications

Welcome to my website! Here, you will find relevant information about my research, teaching, book writing and other activities. As you will see by browsing through this website’s pages, I am particularly interested in the modeling and management of risks in finance, insurance, and economics.

## Recent papers

### Intensity of Preferences for Bivariate Risk Apportionment

with D. Crainich and L. Eeckhoudt
$\frac{(-1)^{n_1+n_2-1} \ u^{(n_1,n_2)}(s,t)}{(-1)^{m_1+m_2-1} \ u^{(m_1,m_2)}(s,t)} \geq \frac{(-1)^{n_1+n_2-1} \ v^{(n_1,n_2)}(s,t)}{(-1)^{m_1+m_2-1} \ v^{(m_1,m_2)}(s,t)}$

Bivariate risk apportionment is the preference for dispersing risks associated with two aspects of individuals’ well-being into different states of the world. In this paper, we propose an intensity measure of this preference by extending to the bivariate case the concept of marginal rate of substitution between risks of different orders introduced in the univariate case by Liu and Meyer (2013). We show that the intensity measure of the preference for bivariate risk apportionment is characterized by bivariate risk attitudes in the sense of Ross. The usefulness of our measures to understand economic choices is illustrated by the analysis of two specific decisions: savings under environmental risk and medical treatment in the presence of diagnostic risks.

Journal of Mathematical Economics

Vol. 88, p. 153–160, 2020

### Regulation Risk

with J. Lévy Véhel and C. Walter
$\text{VaR} \simeq \sigma \left(\frac{C_{\alpha}}{2(1-p)}\right)^{\frac{1}{\alpha}}$

Market risk regulations adopted in response to recent crises aim to reduce financial risks. Nevertheless, a large number of practitioners feel that, if these rules seem to succeed in lowering volatility, they appear to rigidify the financial structure of the economic system and tend to increase the probability of large jumps: prudential rules seem to produce an unexpected effect, the swap between volatility risk and jump risk. The aimed reduction of volatility is accompanied by an increase in the intensity of jumps. The new regulations seem create a new risk. This paper discusses this idea in three ways. First, we introduce a conventionalist framework to put some light on this unexpected effect. Second, we precisely define volatility risk and the intensity of jumps to document the risk swap effect by analysing a daily time series of the SP500 Index. Third, we propose a model which allows one to appreciate a practical consequence of this swap on the risk measures. We conclude by challenging the main objective of regulation: we argue that concentrating on reducing the sole volatility can create a new type of risk which increases the potential losses, that we term regulation risk.

the North American Actuarial Journal

Vol. 24, N°3, p. 463–474, 2020