Standard parametric specifications of Cumulative Prospect theory (CPT) can explain why agents bet on longshots at actuarially unfair odds. However, the standard specification of CPT cannot explain why people might bet on more favoured outcomes, where by construction the greatest volume of money is bet. This article outlines a parametric specification than can consistently explain gambling over all outcomes. In particular we assume that the value function is bounded from above and below and that the degree of loss aversion experienced by the agent is smaller for small-stake gambles (as a proportion of wealth) than usually assumed in CPT. There are a number of new implications of this specification. Boundedness of the value function in CPT implies that the indifference curve between expected-return and win-probability for a given stake will typically exhibit both an asymptote (implying rejection of an infinite gain bet) and a minimum, as the shape of the value function dominates the probability weighting function. Also the high probability section of the indifference curve will exhibit a maximum.
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