Time to wealth goals in capital accumulation

Abstract

This paper considers the problem of continuous investment of capital in risky assets over time. Using a Bayesian framework, a model for asset prices is developed where the current price dynamics depend on the history of realized prices. A dynamic Bayesian fractional Kelly strategy, where the investor rebalances the portfolio based on the performance to date, is shown to be optimal assuming that the risky assets are jointly lognormally distributed. The strategy minimizes the expected time to reach a wealth goal while maintaining a high probability of reaching that goal before falling to a subsistence level of wealth.