Explicit Solutions of Optimal Consumption, Investment and Insurance Problem with Regime Switching

We generalize Merton’s framework by incorporating an insurable loss. Mo-tivated by new insurance products, we allow not only the financial market but also the insurable loss to depend on the regime of the economy. An investor wants to select an optimal consumption, investment, and insurance policy that maximizes his expected total discounted utility of consumption over an infinite time horizon. For the case of hyperbolic absolute risk aver-sion (HARA) utility functions, we obtain the first explicit solutions for opti-mal consumption, investment, and insurance problem 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 econ-omy. Through an economic analysis, we calculate the advantage of buying insurance. We also observe that as long as optimal insurance is nonzero in one regime, investors gain benefits in all regimes from insurance