Abstracts

We consider a stochastic volatility financial model where the asset price process and the volatility process depend on an observable Markov chain. The processes for the asset price and for the stochastic volatility exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor’s expected utility from terminal wealth. To this aim we apply Merton’s approach, i.e. we solve the HJB equations, which in our case correspond to a system of coupled non-linear PDEs. Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic volatility. In the presence of leverage we propose a separable ansatz, which allows us to reduce this case to the one with no leverage. General verification results are also proved. The results are illustrated with the example of the Markov modulated Heston model.