Dynamic Portfolio Selection with Relative Value at Risk Constraint

A portfolio optimization with downside risk based on benchmark is investigated. The expected relative terminal wealth is maximized under a new risk constraint, RVaR, which is defined by a relative wealth process. In a Black-Scholes setting, stochastic analysis method and nonlinear programming theory are used to obtain explicit solutions of the optimal strategies, which include the riskless asset, revised market portfolio and benchmark portfolio. The results exhibit three-fund separation theorem. Numerical examples are presented.