Mathematical Control and Related Fields (MCRF)

Optimal insurance in a changing economy

Pages: 187 - 202, Volume 4, Issue 2, June 2014      doi:10.3934/mcrf.2014.4.187

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Jingzhen Liu - School of Insurance, Central University Of Finance and Economics, Beijing 100081, China (email)
Ka-Fai Cedric Yiu - Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China (email)
Tak Kuen Siu - Cass Business School, City University London, London, EC1Y 8TZ, United Kingdom (email)
Wai-Ki Ching - Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong, China (email)

Abstract: We discuss a general problem of optimal strategies for insurance, consumption and investment in a changing economic environment described by a continuous-time regime switching model. We consider the situation of a random investment horizon which depends on the force of mortality of an economic agent. The objective of the agent is to maximize the expected discounted utility of consumption and terminal wealth over a random future lifetime. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution related to the optimal consumption, investment and insurance is provided. In the cases of a power utility and an exponential utility, we derive analytical solutions to the optimal strategies. Numerical results are given to illustrate the proposed model and to document the impact of switching regimes on the optimal strategies.

Keywords:  Optimal insurance, regime-switching, utility maximization, dynamic programming, regime-switching HJB equations.
Mathematics Subject Classification:  Primary: 93E20; Secondary: 49l20.

Received: March 2012;      Revised: April 2013;      Available Online: February 2014.