Asymptotic minimization of expected time to reach a large wealth level in an asset market game

TL;DR

This paper analyzes a stochastic asset market game and proves that proportional investment strategies asymptotically minimize the expected time to reach a large wealth level, under i.i.d. assumptions.

Contribution

It establishes the asymptotic optimality of proportional investment strategies in a stochastic asset market model with i.i.d. payoffs.

Findings

Proportional investment strategies minimize expected time to wealth target.

Asymptotic optimality holds under i.i.d. asset payoffs.

The model provides insights into optimal investment timing.

Abstract

We consider a stochastic game-theoretic model of a discrete-time asset market with short-lived assets and endogenous asset prices. We prove that the strategy which invests in the assets proportionally to their expected relative payoffs asymptotically minimizes the expected time needed to reach a large wealth level. The result is obtained under the assumption that the relative asset payoffs and the growth rate of the total payoff during each time period are independent and identically distributed.