A model for a large investor trading at market indifference prices. II: Continuous-time case

TL;DR

This paper develops a continuous-time economic model for a large investor trading at market indifference prices, describing the dynamics with a nonlinear stochastic differential equation for market makers' utilities.

Contribution

It introduces a continuous-time framework for large investor trading at utility indifference prices, extending discrete models to stochastic differential equations.

Findings

Model describes market dynamics via nonlinear stochastic differential equations.

Market makers optimize Pareto allocations through competitive quoting.

Transition from simple to continuous strategies is mathematically characterized.

Abstract

We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. As a result, we show that the model's evolution can be described by a nonlinear stochastic differential equation for the market makers' expected utilities.