Moral hazard in dynamic risk management
Dylan Possama├» (Université Paris-Dauphine, France)
Joint work with Jaksa Cvitanic and Nizar Touzi

Wednesday June 4, 11:30-12:00 | session 4.6 | Risk Management | room L

When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. Using a very recent theory of singular changes of measures for Ito processes, we formulate the principal-agent problem in this context, and solve it in the case of CARA preferences.
In that case, the optimal contract is linear in these factors: the contractible sources of risk, including the output, the quadratic variation of the output and the cross-variations between the output and the contractible risk sources. Thus, path-dependent contracts naturally arise when there is moral hazard with respect to risk management. We also provide comparative statics via numerical examples. Finally, we explain how to extend this novel approach to dynamic contracting problems as in Sannikov.

Model Uncertainty and Scenario Aggregation
Mathieu Cambou (EPFL, Switzerland)
Joint work with Damir Filipovic

Wednesday June 4, 12:00-12:30 | session 4.6 | Risk Management | room L

This paper elaborates on model uncertainty and scenario aggregation. An existing approach proposed within the Swiss Solvency Test (SST) is presented and discussed. We then propose a general and coherent framework for scenario aggregation based on divergence minimization from a reference probability measure subject to scenario constraints. The robustness of standard risk measures with respect to changes in the reference probability measure is discussed. This new scenario aggregation approach is illustrated with examples and case studies.

Robust Measurement of Heavy-Tailed Risks: Theory and Implementation
Judith C. Schneider (University of Muenster, Germany)
Joint work with Nikolaus Schweizer

Wednesday June 4, 12:30-13:00 | session 4.6 | Risk Management | room L

Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case in heavy-tailed applications. Moreover, we present a novel, empirical way for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. For heavy-tailed risks, the simulation of the worst case distribution is numerically intricate. We present an SMC (Sequential Monte Carlo) algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach.