A Prospect-Theory Approach to the Kelly Criterion for Fat-Tail Portfolios: The Case of the Student T-Distribution

An analytic approximation is derived for leverage levels that result from optimization of the logarithmic utility function associated with the Kelly criterion. An extension of this approximation, for the case when returns are drawn from a Student t-distribution, is then provided for a prospect-theory approach to the problem, where the log-utility function is replaced by a log-prospect function with power decision weights, intended to give increased weights to low-probability events. It is shown that the traditional fractional-Kelly rule arises as a special case of this prospect-Kelly approach.