Utility maximization in Wiener-transformable markets

TL;DR

This paper addresses utility maximization in a broad class of markets including Gaussian processes with long memory, extending traditional models to better capture real-world price phenomena like constant and variable memory.

Contribution

It introduces Wiener-transformable Gaussian processes and provides a representation for solving utility maximization problems in these markets.

Findings

Includes processes with long memory, fractional Brownian motion, and Gaussian processes with regular covariance.

Provides explicit solutions for various utility functions.

Extends classical models to more accurately reflect market memory effects.

Abstract

We consider a utility maximization problem in a broad class of markets. Apart from traditional semimartingale markets, our class of markets includes processes with long memory, fractional Brownian motion and related processes, and, in general, Gaussian processes satisfying certain regularity conditions on their covariance functions. Our choice of markets is motivated by the well-known phenomena of the so-called "constant" and "variable depth" memory observed in real world price processes, for which fractional and multifractional models are the most adequate descriptions. We introduce the notion of a Wiener-transformable Gaussian process, and give examples of such processes, and their representations. The representation for the solution of the utility maximization problem in our specific setting is presented for various utility functions.