Explicit Solutions of Consumption-Investment Problems in Financial Markets with Regime Switching

We consider a financial market with different regimes that are modeled through an observable continuous-time finite-state Markov chain. The rates of returns and volatilities of the market investing assets, the bank interest rate and the investors' utility of consumption are dependent on the regime of the financial market. Under these settings, an investor taking decisions continuously in time has to select a consumption-investment policy to maximize his expected total discounted utility of consumption until bankruptcy. Using techniques of classical stochastic control adapted to regime switching, we derive the Hamilton-Jacobi-Bellman equation for the problem and obtain explicit optimal consumption and investment policies for specific HARA utility functions. We analyse as well the impact of the regime shifts in the investor's optimal decision.