Certainty equivalence in the continuous-time portfolio-cum-saving model

A model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is considered in which the vector process representing returns to investment is a general semimartingale within dependent increments and the welfare functional has the discounted constant relative risk aversion form. The following results are proved under slight conditions. If suitable variable are chosen, the sure (i.e. non-random) plans form a complete class. If an optimal plan exists, then a sure optimal plan exists, and conversely an optimal sure plan is optimal. The problem of portfolio choice can be separated from the problem of optimal saving. Conditions are given for the uniqueness of the portfolio plan optimal plan.