Filtering and Portfolio Optimization with Stochastic Unobserved Drift in Asset Returns

Fouque, Jean-Pierre; Papanicolaou, Andrew; Sircar, Ronnie

doi:10.2139/ssrn.2304981

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Filtering and Portfolio Optimization with Stochastic Unobserved Drift in Asset Returns

Communications in Mathematical Sciences, 13(4):935-953 (2015).

20 Pages Posted: 2 Aug 2013 Last revised: 26 Jun 2017

See all articles by Jean-Pierre Fouque

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity

Andrew Papanicolaou

North Carolina State University - Department of Mathematics

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: August 1, 2013

Abstract

We consider the problem of filtering and control in the setting of portfolio optimization in financial markets with random factors that are not directly observable. The example that we present is a commodities portfolio where yields on futures contracts are observed with some noise. Through the use of perturbation methods, we are able to show that the solution to the full problem can be approximated by the solution of a solvable HJB equation plus an explicit correction term.

Keywords: portfolio optimization, filtering, Hamilton-Jacobi-Bellman equation, asymptotic approximations

JEL Classification: G12, G13, G17

Suggested Citation: Suggested Citation

Fouque, Jean-Pierre and Papanicolaou, Andrew and Sircar, Ronnie, Filtering and Portfolio Optimization with Stochastic Unobserved Drift in Asset Returns (August 1, 2013). Communications in Mathematical Sciences, 13(4):935-953 (2015)., Available at SSRN: https://ssrn.com/abstract=2304981 or http://dx.doi.org/10.2139/ssrn.2304981