Optimal reinsurance and investment problem in a defaultable market |
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| Authors: | Jianjing Ma Guojing Wang George Xianzhi Yuan |
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| Institution: | 1. Center for Financial Engineering, Soochow University, Suzhou, P.R. China;2. College of Mathematical Sciences, Shandong Institute of Business and Technology, Yantai, P.R. China;3. Institute of Risk Management, School of Mathematics, Tongji University, Shanghai, P.R. China |
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| Abstract: | This article investigates the optimal reinsurance and investment problem involving a defaultable security. The insurer can purchase reinsurance and allocate his wealth among three financial securities: a money account, a stock, and a defaultable corporate bond. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. Using techniques of stochastic control theory, we derive the corresponding Hamilton–Jacobi–Bellman equation and decompose the original optimization problem into a predefault case and a postdefault case. Explicit expressions for optimal strategies and the corresponding value functions are derived, and the verification theorem is given. Finally, we present numerical examples to illustrate our results. |
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| Keywords: | CEV process Defaultable security Hamilton–Jacobi–Bellman equation Jump-diffusion process Reinsurance and investment |
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