Capital growth and survival strategies in a market with endogenous prices

TL;DR

This paper analyzes survival investment strategies in a market with endogenous prices, showing that assuming one's actions determine prices and using a growth optimal approach leads to near-optimal survival over time.

Contribution

It introduces a method for constructing survival strategies in markets with endogenous prices, emphasizing the role of assuming control over prices and using growth optimal strategies.

Findings

Survival strategies can be approximated by assuming one's actions determine prices.

Growth optimal strategies are asymptotically close to survival strategies.

Results hold under the assumption of short-lived assets.

Abstract

We call an investment strategy survival, if an agent who uses it maintains a non-vanishing share of market wealth over the infinite time horizon. In a discrete-time multi-agent model with endogenous asset prices determined through a short-run equilibrium of supply and demand, we show that a survival strategy can be constructed as follows: an agent should assume that only their actions determine the prices and use a growth optimal (log-optimal) strategy with respect to these prices, disregarding the actual prices. Then any survival strategy turns out to be close to this strategy asymptotically. The main results are obtained under the assumption that the assets are short-lived.