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

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. T...

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Bibliographic Details
Published in:Insurance, mathematics & economics Vol. 47; no. 2; pp. 144 - 153
Main Authors: Chen, Shumin, Li, Zhongfei, Li, Kemian
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.10.2010
North Holland Publ. Co
Elsevier
Elsevier Sequoia S.A
Series:Insurance: Mathematics and Economics
Subjects:
Business
Companies
Constraints
Dynamic programming
HJB equation
Insurance
Insurance companies
Investment policy
Investment-reinsurance Ruin probability Value-at-risk HJB equation Lagrangian method
Investments
Investment–reinsurance
Lagrange multiplier
Lagrangian method
Mathematical economics
Probability
Probability theory
Reinsurance
Risk
Risk assessment
Risk management
Ruin probability
Stochastic control theory
Studies
Value-at-risk
Ruin probability
Investment–reinsurance
Lagrangian method
HJB equation
Value-at-risk
ISSN:0167-6687, 1873-5959
Online Access:Get full text
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Summary: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.
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ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2010.06.002