Pathwise optimality for benchmark tracking

Author

Pra, Paolo Dai ; Runggaldier, Wolfgang J. ; Tolotti, Marco

Author_Institution

Dipt. di Matematica Pura ed Applicata, Univ. di Padova, Italy

Volume

49

Issue

3

fYear

2004

fDate

3/1/2004 12:00:00 AM

Firstpage

386

Lastpage

395

Abstract

We consider the problem of investing in a portfolio in order to track or "beat" a given benchmark. We study this problem from the point of view of almost sure/pathwise optimality. We first obtain a control that is optimal in the mean and this control is then shown to be also pathwise optimal. The standard Merton model leads to lognormality of the value process so that it does not possess the required ergodic properties. We obtain ergodicity by transforming the process so that it remains bounded thereby using a method that can be related to a random time change. We furthermore describe a general approach to solve the Hamilton-Jacobi-Bellman equation corresponding to the given problem setup.

Keywords

financial management; investment; optimal control; stochastic processes; Hamilton-Jacobi-Bellman equation; Merton model; almost sure optimality; benchmark tracking; ergodicity; institutional money management; optimal stochastic control; pathwise optimality; portfolio investment; random time change; value process lognormality; Asset management; Cost function; Equations; Exchange rates; Financial management; Infinite horizon; Investments; Optimal control; Portfolios; Stochastic processes;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2004.824467

Filename

1273638