An explicit formula for optimal portfolios in complete Wiener driven markets: a functional It\^o calculus approach

TL;DR

This paper derives an explicit formula for optimal investment portfolios in complete Wiener-driven markets using functional Itô calculus, offering a simpler alternative to Malliavin calculus that requires only an integrability condition.

Contribution

It introduces a novel explicit formula for optimal portfolios utilizing functional Itô calculus, simplifying the derivation process in Wiener-driven markets.

Findings

Provides an explicit formula for optimal portfolios

Uses functional Itô calculus instead of Malliavin calculus

Requires only an integrability condition

Abstract

We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition.