

Principle Seminar of the Department of Probability Theory, Moscow State University
March 14, 2018, Moscow, MSU, auditorium 1224






On a ruin problem for an insurance company investing reserves in the risky actives
Yu. M. Kabanov^{} ^{} Lomonosov Moscow State University

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Abstract:
In the classical CramerLundberg model it is assumed that reserves are invested in constant cost actives. If the model parameters are such that the mean reserve increases then the ruin probability as a function of an initial capital is exponentially small. If reserves are invested in actives with geometric Brownian motion price dynamics then the situation is completely different. In the case of a small volatility the ruin probability decrease as a power function of an initial capital. But for a large volatility the ruin probability is 1. The talk contains the results on ruin probability asymptotics when the risky active price dynamics is a geometric Levy process. The proofs are based on recent results from the implicit renewal theory.

