Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals

TL;DR

This paper analyzes a differential Riccati equation with indefinite coefficients, establishing its solvability and applying it to develop optimal trading strategies that leverage signals and past prices for improved performance.

Contribution

It introduces a novel analysis of indefinite differential Riccati equations and applies this to derive new optimal trading strategies in market making and drift learning.

Findings

Derived a multi-asset market making strategy using signals.

Developed an optimal trading strategy for learning asset drift.

Established existence and uniqueness of solutions for the DRE.

Abstract

We study a differential Riccati equation (DRE) with indefinite matrix coefficients, which arises in a wide class of practical problems. We show that the DRE solves an associated control problem, which is key to provide existence and uniqueness of a solution. As an application, we solve two algorithmic trading problems in which the agent adopts a constant absolute risk-aversion (CARA) utility function, and where the optimal strategies use signals and past observations of prices to improve their performance. First, we derive a multi-asset market making strategy in over-the-counter markets, where the market maker uses an external trading venue to hedge risk. Second, we derive an optimal trading strategy that uses prices and signals to learn the drift in the asset prices.