Optimal Bookmaking

Accepted for publication in European Journal of Operational Research

35 Pages Posted: 9 Jul 2019 Last revised: 6 Mar 2021

See all articles by Matthew Lorig

Matthew Lorig

University of Washington - Applied Mathematics

Zhou Zhou

The University of Sydney - School of Mathematics

Bin Zou

University of Connecticut - Department of Mathematics

Date Written: July 5, 2019

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.

Keywords: HJB equation; optimization; Poisson process; sports betting; stochastic control; utility

Suggested Citation

Lorig, Matthew and Zhou, Zhou and Zou, Bin, Optimal Bookmaking (July 5, 2019). Accepted for publication in European Journal of Operational Research, Available at SSRN: https://ssrn.com/abstract=3415675 or http://dx.doi.org/10.2139/ssrn.3415675

Matthew Lorig

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

Zhou Zhou

The University of Sydney - School of Mathematics

Sydney, 2006
Australia

Bin Zou (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U1009
Department of Mathematics
Storrs, CT 06269-1069
United States

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