# Optimal Bookmaking

## TL;DR

This paper develops a comprehensive framework for continuous-time betting markets, enabling bookmakers to optimize dynamic pricing strategies to maximize expected utility of wealth, with explicit solutions provided for various models.

## Contribution

It introduces a novel continuous-time model for bookmaker decision-making, offering explicit solutions for optimal pricing strategies in diverse market settings.

## Key findings

- Explicit solutions for optimal betting prices
- Characterization of optimal strategies in different models
- Enhanced understanding of bookmaker's utility maximization

## Abstract

We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of bets placed by gamblers. The bookmaker seeks a price process that maximizes his expected (utility of) terminal wealth. We obtain explicit solutions or characterizations to the bookmaker's optimal bookmaking problem in various interesting models.