Robust optimal investment and reinsurance problem for a general insurance company under Heston model

Ya Huang, Xiangqun Yang and Jieming Zhou ()
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Ya Huang: School of Business, Hunan Normal University
Xiangqun Yang: College of Mathematics and Computer Science, Hunan Normal University
Jieming Zhou: College of Mathematics and Computer Science, Hunan Normal University

Mathematical Methods of Operations Research, 2017, vol. 85, issue 2, No 7, 305-326

Abstract: Abstract In this paper, we study a robust optimal investment and reinsurance problem for a general insurance company which contains an insurer and a reinsurer. Assume that the claim process described by a Brownian motion with drift, the insurer can purchase proportional reinsurance from the reinsurer. Both the insurer and the reinsurer can invest in a financial market consisting of one risk-free asset and one risky asset whose price process is described by the Heston model. Besides, the general insurance company’s manager will search for a robust optimal investment and reinsurance strategy, since the general insurance company faces model uncertainty and its manager is ambiguity-averse in our assumption. The optimal decision is to maximize the minimal expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s surplus processes. By using techniques of stochastic control theory, we give sufficient conditions under which the closed-form expressions for the robust optimal investment and reinsurance strategies and the corresponding value function are obtained.

Keywords: Robust control; Ambiguity-averse; Expected utility; Proportional reinsurance (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00186-017-0570-8

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