Subtle price discrimination and surplus extraction under uncertainty

This paper provides a solution to Proebsting's Paradox, an argument that appears to show that the investment rule known as the Kelly criterion can lead a decision maker to invest a higher fraction of his wealth the more unfavorable the odds he faces are and, as a consequence, risk an arbitrarily high proportion of his wealth on the outcome of a single event. The paper shows that a large class of investment criteria, including 'fractional Kelly', also suffer from the same shortcoming and adapts ideas from the literature on price discrimination and surplus extraction to explain why this is so. The paper also presents a new criterion, dubbed the doubly conservative criterion, that is immune to the problem identified above. Immunity stems from the investor's attitudes toward capital preservation and from him becoming rapidly pessimistic about his chances of winning the better odds he is offered.