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.

Author (s) Details

Daniel Akume
Department of Computer Science, University of Buea, P.O. Box 63, Buea, Cameroon.

Bernd Luderer
Faculty of Mathematics, Chemnitz University of Technology, P.O. Box 964, Chemnitz, 09107, Germany.

Ralf Wunderlich
Department of Mathematics, Zwickau University of Applied Sciences, P.O. Box 201037, Zwickau, 08012, Germany.

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