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Optimal reinsurance and investment problem in a defaultable market

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  • Jianjing Ma
  • Guojing Wang
  • George Xianzhi Yuan

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.

Suggested Citation

  • Jianjing Ma & Guojing Wang & George Xianzhi Yuan, 2018. "Optimal reinsurance and investment problem in a defaultable market," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(7), pages 1597-1614, April.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:7:p:1597-1614
    DOI: 10.1080/03610926.2017.1321772
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    Cited by:

    1. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences," Papers 2106.13888, arXiv.org.
    2. Katia Colaneri & Alessandra Cretarola & Benedetta Salterini, 2021. "Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences," Mathematics, MDPI, vol. 9(14), pages 1-27, July.

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