Optimal portfolio strategies under a shortfall constraint

  • D Akuma Department of Computer Science, University of Buea
  • B Luderer Faculty of Mathematics, Chemnitz University of Technology
  • R Wunderlich Department of Mathematics, Zwickau University of Applied Sciences


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 assumed to comprise 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. It is found that the imposition of the constraint curbs investment in the risky assets.


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