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Minimizing the probability of ruin when claims follow Brownian motion with drift. (English) Zbl 1141.91543
Summary: We extend the work of S. Browne [Math. Oper. Res. 20, 937–958 (1995)] and H. Schmidli [Scand. Actuarial J. 2001, No. 1, 55–68 (2001; Zbl 0971.91039)], in which they minimize the probability of ruin of an insurer facing a claim process modeled by a Brownian motion with drift. We consider two controls to minimize the probability of ruin: (1) investing in a risky asset and (2) purchasing quota-share reinsurance. We obtain an analytic expression for the minimum probability of ruin and the corresponding optimal controls, and we demonstrate our results with numerical examples.

MSC:
91B30 Risk theory, insurance (MSC2010)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B28 Finance etc. (MSC2000)
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