INITIAL INVESTMENT CHOICE AND OPTIMAL FUTURE ALLOCATIONS UNDER TIME-MONOTONE PERFORMANCE CRITERIA

The paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called forward investment performance criteria and, in particular, on the time-monotone ones. It is shown that for this class of forward criteria the desired initial allocations completely characterize the future optimal investment strategies. The analysis uses the connection between a nonlinear equation, satisfied by the local risk tolerance, and the backward heat equation. Complete solutions are provided as well as various examples.