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    STUDIA MATHEMATICA - Issue no. 4 / 2008  
         
  Article:   OPTIMAL DYNAMIC PORTFOLIOS UNDER A TAIL CONDITIONAL EXPECTATION CONSTRAINT.

Authors:  DANIEL AKUME, GUY MERLIN MBAKOP.
 
       
         
  Abstract:  We consider a portfolio problem when a tail conditional expectation 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 constraint into the resolution framework. A numerical method is applied to obtain an approximate solution to the problem. We find that the imposition of the tail conditional expectation constraint when risky assets evolve following a log-normal distribution, curbs investment in the risky assets and increases consumption.  
         
     
         
         
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