Abstract

AbstractAn entrepeneur has a given initial fortune and faces the following situation: during any time period he may invest various amounts of his available fortune in various alternatives (differing from interval to interval) and keep the remainder of his money as a reserve fund; The alternatives materialize and pay off according to a probability distribution in which occurrences in different time intervals are independent. We analyze the problem of finding the investment policies (that is, the division of funds during every time interval between the investment alternatives and the reserve) that will make the long‐run growth of the entrepeneur's fortune as rapid as possible.

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