Optimal Market Making Based on the Hamilton-Jacobi-Bellman Equation-Integral Utility with a Discount

9 Pages Posted: 15 Mar 2017 Last revised: 17 Mar 2017

Atsunari Konishi

KEK Theory Center

Date Written: March 14, 2017

Abstract

We derive optimal spreads for market makers based on the Hamilton-Jacobi-Bellman equation with an integral utility function which takes inventory risk, volatility risk and a discount into account. A discount is introduced so that we can obtain an optimal control in T → ∞ limit, i.e. an optimal control that does not depend on the terminal time. We show that a difference between market buy and sell order intensity acts as a drift. In the limit T → ∞, terms proportional to Tt, a difference between current time and the terminal time, is replaced by ω −1 , an inverse discount factor. We then perform Monte Carlo simulation using obtained optimal spreads for various risk aversion parameter and see that there is “optimal” risk aversion parameter.

Keywords: Market Making, Optimal Spreads, Hamilton-Jacobi-Bellman Equation

Suggested Citation

Konishi, Atsunari, Optimal Market Making Based on the Hamilton-Jacobi-Bellman Equation-Integral Utility with a Discount (March 14, 2017). Available at SSRN: https://ssrn.com/abstract=2932632

Atsunari Konishi (Contact Author)

KEK Theory Center ( email )

1-1 Oho, Ibaraki
Tsukuba, 305-0801
Japan

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