A continuous-time asset market game with short-lived assets

TL;DR

This paper models a continuous-time investment market with short-lived assets, deriving conditions for wealth process solutions and identifying an optimal growth strategy that outperforms others asymptotically.

Contribution

It formulates a stochastic equation for wealth dynamics and demonstrates the existence of an optimal growth portfolio strategy in a market with endogenous prices.

Findings

Existence of solutions to the wealth process stochastic equation

Identification of a strategy that guarantees relative wealth growth

Other strategies' relative wealth vanish asymptotically

Abstract

We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show that there exists a strategy such that the logarithm of the relative wealth of an investor who uses it is a submartingale regardless of the strategies of the other investors, and the relative wealth of any other essentially different strategy vanishes asymptotically. This strategy can be considered as an optimal growth portfolio in the model.