Discrete gambles Theoretical study - Johan Eklund:

Abstract: Given a gamble opportunity with a positive expected return, the question to be asked is: How much money should I gamble?In this thesis, we study how a gambler who holds a general expo-power utility function allocates wealth in discrete gambles. The analyzed gambles are the following: a single binary gamble, equivalent to betting on a tennis match, a double binary gamble, equivalent to betting on two simultaneous tennis matches, and a discrete financial market gamble, equivalent to betting on a financial asset with a discrete outcome distribution. We derive analytical expressions that can be used to approximate utility-optimal bet allocations for any specified expo-power utility function. We propose a general approximation formula to obtain bet allocations at large wealth levels. The Newton-Raphson method is applied to locate optimal bet allocations at lower wealth levels.The main motivation for the thesis is to provide analytical results that enable von Neumann-Morgenstern rational gamblers to establish optimal bet allocation strategies.