Adapting to a Market Shock: Optimal Sequential Market-Making

We study the profit-maximization problem of a monopolistic market-maker. The sequential decision problem is hard 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. The algorithm leads to a surprising insight: an optimal monopolist can provide more liquidity than perfectly competitive market-makers, because a monopolist is willing to absorb initial losses in order to learn a new valuation rapidly so she can extract higher profits later.