Dynamic Portfolio Selection under Conditional Capital at Risk Constraint

In this paper, we investigate the dynamic optimal portfolio selection. In a Black-Scholes setting, a conditional capital at risk constraint is imposed continuously over time. Making use of conditional information, the risk of trading portfolio is reevaluated dynamically to influence the investment decision. We apply the dynamic programming technique and optimal theory to obtain the optimal constrained portfolio allocation strategies in closed form. We find that two-fund separation also holds and the proportions invested in risky assets are lower than they would have been without the risk constraint. Numerical examples are presented.