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Ruin probabilities under general investments and heavy-tailed claims. (English) Zbl 1303.91091

Summary: The asymptotic decay of finite time ruin probabilities is studied. An insurance company is considered that faces heavy-tailed claims and makes investments in risky assets whose prices evolve according to quite general semimartingales. In this setting, the ruin problem corresponds to determining hitting probabilities for the solution to a randomly perturbed stochastic integral equation. A large deviation result for the hitting probabilities is derived that holds uniformly over a family of semimartingales. This result gives the asymptotic decay of finite time ruin probabilities under sufficiently conservative investment strategies, including ruin-minimizing strategies. In particular, as long as the insurance company invests sufficiently conservatively, the investment strategy has only a moderate impact on the asymptotics of the ruin probability.

MSC:

91B30 Risk theory, insurance (MSC2010)
60F10 Large deviations
60G48 Generalizations of martingales
60G70 Extreme value theory; extremal stochastic processes
60H20 Stochastic integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
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