# Analytic solutions in a continuous-time financial market model

## TL;DR

This paper introduces a continuous-time heterogeneous agent market model with fundamental traders and chartists, providing analytical solutions for stability, mean reversion, and strategy profitability, advancing understanding of market dynamics.

## Contribution

It offers a novel analytical framework for stochastic market models with heterogeneous agents, enabling explicit stability and profitability analysis.

## Key findings

- More prevalent trader types achieve higher returns
- Conditions for price stability and mean reversion are derived
- Analytic formulas link population ratios to market outcomes

## Abstract

We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price dynamics and profitability either within deterministic models or by simulation. Our novel formulation lends itself to analytic treatment even in the stochastic case. We prove conditions for the (stochastic) stability of the price process, and also for the price to mean-revert to the fundamental value. Assuming stability, we derive analytic formulae on how the population ratios influence price dynamics and the profitability of the strategies. Our results suggest that whichever trader type is more present in the market will achieve higher returns.