Optimal portfolio strategies under a shortfall constraint

  • D Akume
  • B Luderer
  • R Wunderlich
Keywords: Portfolio optimization, value-at-risk, quadratic utility, tail conditional expectation.


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 nancial 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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eISSN: 0529-191-X