Explicit Solutions for Optimal Insurance Problems in Regime Switching Frameworks

The paper treats the generalized Merton-type optimal consumption invest-ment problem for a financial market whose characterizing parameters depend on the regime of theeconomy. In particular, we consider an agent which controls both his consumption and invest-ment, as well as an insurance contract, and whose objective is to maximize the total discountedutility of consumption over an infinite horizon. In the case of Hyperbolic Absolute Risk Aversion(HARA) utility functions it is possible to obtain explicit solutions to the optimal consumption,investment and insurance problems, showing that the optimal strategies depend on the state of theeconomy. Exploiting latter result we perform a novel financial analysis assuming that the economyis characterized by three volatility regimes, also studying the impact of adding an exogenous wagein the investor’s wealth process.