Calculating Risk Neutral Probabilities and Optimal Portfolio Policies in a Dynamic Investment Model with Downside Risk Control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio's worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifing the optimal terminal wealth and a stochastic linear programming model replicating the identified optimal portfolio. The replicating portfolio coincides with the optimal solution to the investor's problem if the market is frictionless. The multiperiod stochastic linear programming model is designed to test for the existence of arbitrage opportunities and its dual solutions generate all risk neutral probability measures.

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