Experimental Study on Optimal Portfolio Strategies under a Shortfall Constraint

We impose dynamically, a shortfall constraint in terms of Tail Conditional Expectation on the portfolio
selection problem in continuous time, in order to obtain optimal strategies. The financial market
is composed of n risky assets driven by geometric Brownian motion and one risk-free asset. The
method of Lagrange multipliers is combined with the Hamilton-Jacobi-Bellman equation to insert the
constraint into the resolution framework. The constraint is re-calculated at short intervals of time
throughout the investment horizon. A numerical method is applied to obtain an approximate solution
to the problem. We find that the imposition of the constraint curbs investment in the risky assets.