Optimal consumption and portfolio policies for important jump events: modeling and computational considerations

While the volatility of portfolios are often modeled by continuous Brownian motion processes, discontinuous jump processes are more appropriate for modeling important external events that significantly affect the prices of financial assets. Here the discontinuities jump processes are modeled by state and control dependent compound Poisson processes, such that the random jumps come at the times of a pure Poisson process with jump amplitudes that are randomly distributed. The optimal consumption and investment portfolio policy formulation is in terms of stochastic differential equations with optimal discounted utility objectives. This paper was motivated by a recent paper of Rishel (1999) concerning portfolio optimization when prices are dependent on external events. However, the model has been significantly generalized for realistic computational considerations and computations ate illustrated with a simple jump model