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Probability and Computational Finance Seminar
Jin Ma
University of Southern California
Title: Ruin Problems under Model Uncertainty

Abstract: In this talk I will discuss some ruin problems for insurance models with investment, in a general market framework that contains uncertainties on both market volatility and claim frequency. The problem naturally leads to the evaluation of the ruin probability under the so-called $G$-expectation, a non-linear expectation developed recently by S. Peng. We prove that the claim process can be naturally described as a class of ``$G$-Compound Poisson process", a special case of the so-called $G$-L\'evy process studied by Hu-Peng (2010). Such a relation, however, does not seem to be obvious from the original definition of a nonlinear expectation. We also establish the relationship between the study of asymptotic behavior of a ruin probability and the sample path large deviation principle (LDP) of a ``storage process", defined as a special type of reflected SDE with discontinuous paths, under the $G$-framework. We show that the asymptotic Lundberg bounds can be determined by the rate function of the LDP. Some related issues for the market models under $G$-expectations will be discussed as well.

This is a joint work with Xin Wang.

Date: Monday, April 9, 2012
Time: 5:00 pm
Location: Wean Hall 5409
Submitted by:  Dmitry Kramkov