NDLI: Optimal Control with Restrictions for a Diffusion Risk Model Under Constant Interest Force

Content Provider	Springer Nature Link
Author	Guo, Junyi Peng, Xiaofan Bai, Lihua
Copyright Year	2015
Abstract	In this paper, we study optimal dividend problems in a diffusion risk model for two different cases depending on whether reinsurance is incorporated. In either case, the dividend rate is bounded above by a constant, and the company earns investment income at a constant force of interest. Unlike existing approaches in the literature dealing with optimal problems with interest, we allow the force of interest to be greater than the discount factor, and we use a different method to solve the corresponding Hamilton–Jacobi–Bellman (HJB) equation instead of introducing a confluent hypergeometric function. We conclude that the optimal dividend policy is of a threshold type and show that the corresponding dividend barrier is nondecreasing in the dividend rate bound. In cases where there is no reinsurance, we construct an auxiliary reflecting control problem to find the nonzero dividend barrier. If proportional reinsurance is purchased, the optimal reinsurance strategy looks somewhat strange. The optimal retention level of risk first increases monotonically with risk reserve to some possible value (less than $$1$$ ) and then stays at level $$1$$ for a while or, if $$1$$ has been reached, finally, it decreases to 0.
Ending Page	136
Page Count	22
Starting Page	115
File Format	PDF
ISSN	00954616
e-ISSN	14320606
Journal	Applied Mathematics and Optimization
Issue Number	1
Volume Number	73
Language	English
Publisher	Springer US
Publisher Date	2015-03-04
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Economics Systems Theory, Control Risk theory, insurance Theoretical, Mathematical and Computational Physics Optimal dividend Proportional reinsurance Interest Mathematical Methods in Physics Calculus of Variations and Optimal Control; Optimization HJB equation Optimal stochastic control Numerical and Computational Physics Interest rates (stochastic models)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization

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