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

TL;DR

This paper derives explicit solutions for an investor's optimal consumption, investment, and insurance strategies in a regime-switching economy, highlighting how economic states influence insurance decisions.

Contribution

It provides the first explicit solutions for combined consumption, investment, and insurance problems with regime switching under HARA utility functions.

Findings

Optimal insurance is either no-insurance or deductible insurance.

The optimal policy varies significantly with economic regime.

Buying insurance offers measurable economic advantages.

Abstract

We consider an investor who wants to select her/his optimal consumption, investment and insurance policies. Motivated by new insurance products, we allow not only the financial marke but also the insurable loss to depend on the regime of the economy. The objective of the investor is to maximize her/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.