Optimal dividend problem with a nonlinear regular-singular stochastic control

Mi Chen, Xiaofan Peng and Junyi Guo

Insurance: Mathematics and Economics, 2013, vol. 52, issue 3, 448-456

Abstract: In this paper, a problem with a nonlinear regular-singular stochastic control is studied for a big insurance portfolio. We assume that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problem nonlinear. Both non-cheap and cheap reinsurance are investigated. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. Bounded dividend rates and unbounded dividend rates are considered. In both cases, explicit expressions for the value function and the corresponding optimal strategies are obtained. Finally, a numerical example is presented, which shows the impacts of risk aversion of the reinsurance company on the optimal value function and the retention level for reinsurance.

Keywords: Dividend; Proportional reinsurance; Non-cheap reinsurance; Cheap reinsurance; Exponential premium principle (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:52:y:2013:i:3:p:448-456

DOI: 10.1016/j.insmatheco.2013.02.010

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