Applied Mathematics & Optimization

, Volume 77, Issue 2, pp 229–252 | Cite as

Risk Sensitive Control of the Lifetime Ruin Problem

  • Erhan Bayraktar
  • Asaf Cohen


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.


Probability 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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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