# Abstracts

**A Non-cyclical Capital Adequacy Rule and the Aversion of Systemic Risk**

*Raphael Douady (University Paris 1-Sorbonne, France)*

Wednesday June 4, 11:30-12:00 | session 4.3 | Risk Measures | room EF

We present in this note a method for computing the regulatory capital of financial institutions, along with the Basel Committee requirements, which avoids the pitfalls of the Value-at-Risk and, in particular, the fact that – as observed during 2008 crisis – it aggravates systemic risk rather than preventing it. The computation is based on stress testing, with the following principles: (i) market scenarios are defined by the regulator; (ii) sensitivities are estimated by each institution, as well as the impact of scenarios defined by the regulator and reported to it; (iii) the regulator not only counts the number of violations of the risk reporting but also their size; (iv) the regulatory capital is a multiple of the worst stress test, where the multiplier depends on the size and the frequency of the violations. By letting the institutions estimate their sensitivities to extreme market shifts, the regulator not only avoids a costly burden, but also keeps institutions responsible for their reporting. On the other hand, by keeping control on the list of stress tests involved in the computation of the capital, the regulator offers itself a very strong lever to prevent speculative bubbles, by making them costly in terms of capital requirements.

**Backward Stochastic Difference Equations for Dynamic Convex Risk Measures on a Binomial Tree**

*Robert Elliott (University of Calgary, Canada)*

Wednesday June 4, 12:00-12:30 | session 4.3 | Risk Measures | room EF

The classical familiar framework used to introduce financial pricing is the binomial model. The talk will discuss several more advanced concepts in this simple framework. These will include martingale representation, Malliavin derivatives, backward stochastic difference equations and dynamic risk measures. The latter are introduced using non linear expectations which are the solutions of backward stochastic difference equations.

**General Uncertainty Averse Preferences**

*Samuel Drapeau (TU Berlin, Germany)*

Wednesday June 4, 12:30-13:00 | session 4.3 | Risk Measures | room EF

We study the preferences of agents for diversification and better outcomes when they are facing both, in Frank Knight's formulation, measurable as well as unmeasurable uncertainty. Following Anscombe and Aumann, such a situation can be modeled by preferences expressed on stochastic kernels, that is scenario dependent lotteries. By means of automatic continuity methods based on Banach-Dieudonné's theorem on Fréchet spaces, we provide a robust representation. This gives us some insight into the nature of uncertainty aversion these preferences are expressing. We further investigate under which conditions these two intricate dimensions of uncertainty can be disentangle into a distributional uncertainty, in the direction of von Neumann and Morgenstern's theory, and a probability model uncertainty, in the spirit of risk measures. These results allow in particular to address both Allais as well as Elsberg's paradox.