Optimal reinsurance and investment problem in a defaultable market

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.

KEYWORDS:

• CEV process
• Defaultable security
• Hamilton–Jacobi–Bellman equation
• Jump-diffusion process
• Reinsurance and investment.

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B30
• 91G40
• 93E20

Additional information

Funding

This work was supported by National Natural Science Foundation of China (11371274) and Shandong Natural Science Foundation (ZR2013AM011).