Communications in Mathematical Sciences

Volume 13 (2015)

Number 4

Special Issue in Honor of George Papanicolaou’s 70th Birthday

Guest Editors: Liliana Borcea, Jean-Pierre Fouque, Shi Jin, Lenya Ryzhik, and Jack Xin

Filtering and portfolio optimization with stochastic unobserved drift in asset returns

Pages: 935 – 953



Jean-Pierre Fouque (Department of Statistics & Applied Probability, University of California at Santa Barbara)

Andrew Papanicolaou (School of Mathematics & Statistics, University of Sydney, Australia)

Ronnie Sircar (ORFE Department, Princeton University, Princeton, New Jersey, U.S.A.)


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.


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

2010 Mathematics Subject Classification

35C20, 35Q93, 60G35, 91G20

Published 12 March 2015