Market Making & Stochastic Optimal Control in Live Sports Betting

Abstract

In this senior thesis, we provide a stochastic analysis approach to the live sports betting context. We rigorously characterize the optimal behavior of a bookmaker and bettors of different types in a betting market for a stochastically evolving underlying sports game. We derive the optimal strategies and the dynamics satisfied by expected terminal wealth through partial differential equations of Hamilton-Jacobi type. We aimed for the thesis to be as mathematically comprehensive and rigorous as possible through techniques from functional analysis and measure theory. Moreover, we fully characterize Stackelberg equilibria for markets with bettors of both homogeneous and heterogeneous types.