An explicit solution for optimal investment problems with autoregressive prices and exponential utility

TL;DR

This paper derives an explicit optimal investment strategy for an investor with exponential utility in a market where stock prices follow an autoregressive Gaussian process, analyzing its performance over long horizons and linking it to the process's memory.

Contribution

It provides the first explicit solution connecting the autoregressive memory of asset prices to investor satisfaction levels.

Findings

Explicit optimal strategy derived for autoregressive Gaussian prices

Performance analysis over infinite trading horizon

Established link between process memory and investor utility

Abstract

We calculate explicitly the optimal strategy for an investor with exponential utility function when the stock price follows an autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends to infinity. Dependence of asymptotic performance on the autoregression parameter is determined. This provides, to the best of our knowledge, the first instance of a theorem linking directly the memory of the asset price process to the attainable satisfaction level of investors trading in the given asset.