%0 Journal Article
%T Dynamic shortfall constraints for optimal portfolios
%A Daniel Akume
%A Bernd Luderer
%A Ralf Wunderlich
%J Surveys in Mathematics and its Applications
%D 2010
%I University Constantin Brancusi of Targu-Jiu
%X 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 calculated for short intervals of time and imposed as risk constraint dynamically. 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 diverts the wealth to consumption.
%K Portfolio optimization
%K Risk management
%K Dynamic risk constraints
%K Tail Conditional Expectation
%U http://www.utgjiu.ro/math/sma/v05/p12.pdf