Optimal reinsurance and investment with unobservable claim size and intensity

Zhibin Liang and Erhan Bayraktar

Insurance: Mathematics and Economics, 2014, vol. 55, issue C, 156-166

Abstract: We consider the optimal reinsurance and investment problem in an unobservable Markov-modulated compound Poisson risk model, where the intensity and jump size distribution are not known but have to be inferred from the observations of claim arrivals. Using a recently developed result from filtering theory, we reduce the partially observable control problem to an equivalent problem with complete observations. Then using stochastic control theory, we get the closed form expressions of the optimal strategies which maximize the expected exponential utility of terminal wealth. In particular, we investigate the effect of the safety loading and the unobservable factors on the optimal reinsurance strategies. With the help of a generalized Hamilton–Jacobi–Bellman equation where the derivative is replaced by Clarke’s generalized gradient as in Bäuerle and Rieder (2007), we characterize the value function, which helps us verify that the strategies we constructed are optimal.

Keywords: Markov-modulated compound Poisson process; Proportional reinsurance; Optimal investment (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (35)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:55:y:2014:i:c:p:156-166

DOI: 10.1016/j.insmatheco.2014.01.011

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