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 with independent increments and the welfare functional has the 'discounted constant relative risk aversion' form. The following results are proved under slight conditions. If suitable variants 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 generating a given returns process and for the uniqueness of an optimal plan.
