Explicit solutions of optimal consumption,investment and insurance problems with regime switching |
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| Institution: | 1. School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210023, China;2. Department of Mathematics, University of Michigan, MI 48109, United States;1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;2. Finance Discipline Group, UTS Business School, The University of Technology, Sydney, NSW, Australia;3. Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;1. School of Business, Hunan Normal University, Changsha, Hunan, 410081, PR China;2. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP)(Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, PR China;1. Department of Computing Science, School of Mathematics and Statistics, Xi''an Jiaotong University, 710049 Xi''an, Shaanxi, PR China;2. Rowe School of Business, Dalhousie University, 6100 University Avenue, Halifax, Canada B3H3J5 |
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| Abstract: | We consider an investor who wants to select his optimal consumption, investment and insurance policies. Motivated by new insurance products, we allow not only the financial market but also the insurable loss to depend on the regime of the economy. The objective of the investor is to maximize his expected total discounted utility of consumption over an infinite time horizon. For the case of hyperbolic absolute risk aversion (HARA) utility functions, we obtain the first explicit solutions for simultaneous optimal consumption, investment, and insurance problems when there is regime switching. We determine that the optimal insurance contract is either no-insurance or deductible insurance, and calculate when it is optimal to buy insurance. The optimal policy depends strongly on the regime of the economy. Through an economic analysis, we calculate the advantage of buying insurance. |
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| Keywords: | Economic analysis Hamilton–Jacobi–Bellman equation Insurance Regime switching Utility maximization |
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