MCFAM Seminar - A mathematical analysis of optimal portfolio on finite and small-time horizons

Speaker: Indranil SenGupta

Abstract: In this presentation, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change from its current value. We consider an incomplete stochastic volatility market model that is driven by both a Brownian motion and a jump process. We show a closed-form formula for an approximation to the optimal portfolio in a small-time horizon. We also prove the accuracy of the approximation formulas. Finally, we provide a procedure for generating a close-to-optimal portfolio for a finite time horizon.