Ruin Problems under Model Uncertainties

Mathematical Finance/Financial Engineering Seminar
Wednesday, October 12, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 006
School of Mathematics, University of Southern California

Hosted by Christian Houdre and Liang Peng

In this work we study the ruin problem for a generalized Cramer-Lundberg reserve model with investments, under the modeling (volatility and claim intensity) uncertainty. We formulate the problem in terms of the newly developed theory on G-Expectation, initiated by S. Peng (2005). More precisely, we recast the problem as to determine the ruin probability under a G-expectation for a reserve process with a G-Compound Poisson type claim process, and perturbed by a G-Brownian motion. We show that the Lundberg bounds for a finite time ruin probability can still be obtained by an exponential $G$-martingale approach, and that the asymptotic behavior of the ruin, as the initial endowment tends to infinity, can be analyzed by the sample path large deviation approach in a G-expectation framework, with respect to the corresponding storage process. This is a joint work with Xin Wang.