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

17 Pages Posted: 23 Sep 2008 Last revised: 8 Oct 2008

Date Written: September 15, 2008

Abstract

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.

Keywords: Kelly criterion, prospect theory, leverage, fat tails, t-distribution, Student t-distribution

JEL Classification: C49, D81, D84

Suggested Citation

Osorio, Roberto, A Prospect-Theory Approach to the Kelly Criterion for Fat-Tail Portfolios: The Case of the Student T-Distribution (September 15, 2008). Available at SSRN: https://ssrn.com/abstract=1271373 or http://dx.doi.org/10.2139/ssrn.1271373

Roberto Osorio (Contact Author)

DUNN Capital Management ( email )

309 SE Osceola St Ste 350
Stuart, FL 34994-2250
United States
7727813289 (Phone)

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