Adapting to a Market Shock: Optimal Sequential Market-Making

We study the profit-maximization problem of a monopolistic market-maker who sets two-sided prices in an asset market. The sequential decision problem is hard to solve because the state space is a function. We demonstrate that the belief state is well approximated by a Gaussian distribution. We prove a key monotonicity property of the Gaussian state update which makes the problem tractable, yielding the first optimal sequential market-making algorithm in an established model. The algorithm leads to a surprising insight: an optimal monopolist can provide more liquidity than perfectly competitive market-makers in periods of extreme uncertainty, because a monopolist is willing to absorb initial losses in order to learn a new valuation rapidly so she can extract higher profits later.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Sanmay Das, Malik Magdon-Ismail
• Keywords: Gaussian State Update, Information Technology, NIPS 2008, Optimal Sequential Market-making, Sequential Decision Problem