Optimal investment-reinsurance policy for an insurance company with VaR constraint

Shumin Chen, Zhongfei Li and Kemian Li

Insurance: Mathematics and Economics, 2010, vol. 47, issue 2, 144-153

Abstract: This paper investigates an investment-reinsurance problem for an insurance company that has a possibility to choose among different business activities, including reinsurance/new business and security investment. Our main objective is to find the optimal policy to minimize its probability of ruin. The main novelty of this paper is the introduction of a dynamic Value-at-Risk (VaR) constraint. This provides a way to control risk and to fulfill the requirement of regulators on market risk. This problem is formulated as an infinite horizontal stochastic control problem with a constrained control space. The dynamic programming technique is applied to derive the Hamilton-Jacobi-Bellman (HJB) equation and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Closed-form expressions for the minimal ruin probability as well as the optimal investment-reinsurance/new business policy are derived. It turns out that the risk exposure of the insurance company subject to the dynamic VaR constraint is always lower than otherwise. Finally, a numerical example is given to illustrate our results.

Keywords: Investment-reinsurance; Ruin; probability; Value-at-risk; HJB; equation; Lagrangian; method (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (31)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-6687(10)00071-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:47:y:2010:i:2:p:144-153

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().