From One-Fund Separation to One-Derivative Separation The Stochastic-Solution Portfolio Choice Model under Risk

Abstract

Assuming appropriate infinite-state model, we consider a previously un-examined stochastic-solution choice problem which includes known constant-solution choice problem as a degenerated case. We suggest dependence conditions on risks to range or explicitly solve for the stochastic solution with a general optimization standard. This updated perspective not only disentangles a popular misconception on the existence of solutions to many existing models but also solves the problem of finding the optimally customizable derivative which is only examined in a few works assuming specific optimization standard and distribution of the risks.