Optimal portfolio with unobservable market parameters and certainty equivalence principle

TL;DR

This paper develops an explicit solution for optimal investment strategies in incomplete markets with unobservable parameters, using historical data and prior distributions, applicable to power utilities and Markovian settings.

Contribution

It introduces a novel approach to portfolio optimization with unobservable market parameters, providing explicit solutions and new estimation techniques.

Findings

Explicit solutions for power utility cases

New estimates and filters for appreciation rates

Applicable to Markovian market models

Abstract

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather use historical stock prices and an a priory given distribution of the appreciation rates. An explicit solution is found for case of power utilities and for a case when the problem can be embedded to a Markovian setting. Some new estimates and filters for the appreciation rates are given.