A Dynamic Portfolio Model With The Downside Risk

This paper considers a portfolio problem with the downside risk. The utility brought from the worst-case outcome is taken as part of the whole objective utility to control the downside risk. An optimal policy which is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets is obtainable in the model. Applying the Black-Scholes formula, a closed-form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The paper also tests the effect of risk control under the frame of VaR. The analysis provides a useful method of converting an investment problem to an option pricing model.