Optimal Bookmaking with CRRA Utility: Existence, Uniqueness, and Numerical Methods
Session Title
Gambling Mathematics: Quantitative Finance
Presentation Type
Paper Presentation
Start Date
26-5-2026 12:00 AM
Abstract
We extend the optimal bookmaking framework of Lorig, Zhou, and Zou (2021) to incorporate Constant Relative Risk Aversion (CRRA) utility functions. While the original paperhandles risk-neutral and exponential utility cases with explicit solutions, the CRRA case leads to fully coupled nonlinear optimality conditions that require numerical solution. We establish existence and uniqueness of optimal prices, prove convergence of fixed-point and Newton-type iterative methods, and develop perturbation approximations around the risk-neutral limit. Monte Carlo simulations compare risk-adjusted performance across all three utility specifications. Code and reproducible experiments are available at the accompanying repository.
Optimal Bookmaking with CRRA Utility: Existence, Uniqueness, and Numerical Methods
We extend the optimal bookmaking framework of Lorig, Zhou, and Zou (2021) to incorporate Constant Relative Risk Aversion (CRRA) utility functions. While the original paperhandles risk-neutral and exponential utility cases with explicit solutions, the CRRA case leads to fully coupled nonlinear optimality conditions that require numerical solution. We establish existence and uniqueness of optimal prices, prove convergence of fixed-point and Newton-type iterative methods, and develop perturbation approximations around the risk-neutral limit. Monte Carlo simulations compare risk-adjusted performance across all three utility specifications. Code and reproducible experiments are available at the accompanying repository.