OPTIMAL DYNAMIC PORTFOLIOS UNDER A TAIL CONDITIONAL EXPECTATION CONSTRAINT

Résumé

Abstract. We consider a portfolio problem when a tail conditional ex-pectation constraint is imposed. The financial market is composed of n risky assets driven by geometric Brownian motion and one risk-free asset. The tail conditional expectation is derived, re-calculated at short intervals of time and imposed continuously. The method of Lagrange multipliers is combined with the Hamilton-Jacobi-Bellman equation to insert the con-straint into the resolution framework. A numerical method is applied to obtain an approximate solution to the problem. We find that the imposi-tion of the tail conditional expectation constraint when risky assets evolve following a log-normal distribution, curbs investment in the risky assets and increases consumption. 1.