Optimal Liquidity Provision at the Best Bid and Ask

Summary

The document analyzes a small investor who supplies liquidity by posting at the best bid and ask in a limit order market. It describes an explicit determination of the investor’s optimal policy and welfare under small spreads and frequent order arrivals from other market participants.

The framework allows the mid price, spread, and order flow to follow general dynamics, and it accommodates arbitrary preferences for the liquidity provider. This makes the setup relevant to market-making decisions where execution opportunities and price movement interact. The description does not specify a particular solution formula, calibration, data set, or empirical performance result, so it establishes the scope of a general model rather than evidence that a given posting policy will work in a specific market.

Key ideas

• The setting is a small investor posting liquidity at the best bid and ask.
• The analysis derives an optimal policy and welfare under small spreads and frequent incoming orders.
• The framework permits general dynamics for mid price, spread, and order flow.
• The liquidity provider’s preferences can be modeled arbitrarily.

Tags

# Optimal Liquidity Provision


# Optimal Liquidity Provision









A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as for arbitrary preferences of the liquidity provider under consideration.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.