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MSRI-UP Colloquium: Viscosity Solution Methods and the Problem of Ruin July 15, 2015 (10:30 AM PDT - 11:30 AM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Khalilah Beal (University of California)
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In this talk, we will investigate the problem of “collective ruin” in classical risk theory, which models the risk of an insurance business. We model the probability that a reserve remains nonnegative with a scaled integro-differential equation (IDE). Introducing a gauge parameter allows consideration of solutions for large initial reserves and motivates our discussion of perturbation. Using generalized solutions, as opposed to classical solutions, allows a broad class of collective risk problems to be studied. We begin with a discussion of viscosity solutions.

The results of this talk extend work of Knessl, Mangel, Peters, and others who treat cases of the main problem with constant premiums and/or smooth distributions of claims.

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