Optimal Strategies for Prudent Investors

TL;DR

This paper models a prudent investment strategy that maximizes exponential growth while ensuring the investor's economic level never declines, using stochastic processes and analytical solutions.

Contribution

It introduces an optimal investment strategy based on maximizing growth rate with a fixed fraction of maximum wealth, providing analytical expressions for growth and fluctuations.

Findings

Derived analytical formulas for growth rate and fluctuations.

Identified optimal fraction of wealth to invest for maximum growth.

Provided a stochastic model for prudent investment strategies.

Abstract

We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed $\a$. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.