PORTFOLIO OPTIMIZATION

UNDER ASYMMETRIC ASSUMPTIONS

WITH MULTIPLE SCENARIOS

A NEW FORMULATION

Suppose scenarios 1 through K may occur with probabilities p_k (not necessarily all equal), and have different return profiles, downside worst cases and covariances. One then solves the following Maximum CE value problem for a range of risk tolerance values.

Note that the mean, variance and downside parameters are computed for each scenario, these are used in the final constraint set to compute the CE-value for each scenario, and then the CE-values are combined in the objective function, taking into account the probability of each scenario, using the CE function for finite discrete gambles.  This becomes a nonlinear programming problem which can as usual be solved for a range of risk tolerance values so as to map out the Maximal CE-Value Frontier for the multiple scenario portfolio allocation problem.