Risk Sensitive Control of the Lifetime Ruin Problem
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We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black–Scholes market that includes a risky asset and a riskless asset. We present a differential game that governs the limit behavior. We solve it explicitly and use it in order to find an asymptotically optimal policy.
KeywordsProbability of lifetime ruin Optimal investment Risk sensitive control Large deviations Differential games
We thank the two anonymous referees, the AE and Huyên Pham for insightful comments, which helped us improve our paper. We are also grateful to Virginia Young for many discussions that we had on the subject. This research is supported in part by the National Science Foundation through the DMS-1613170 Grant.
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