A MARKOVIAN APPROXIMATED SOLUTION TO A PORTFOLIO MANAGEMENT PROBLEM



provided by Research Papers in Economics


A MARKOVIAN APPROXIMATED SOLUTION TO A
PORTFOLIO MANAGEMENT PROBLEM *

Jacek B. Krawczyk

Victoria University of Wellington, PO Box 600, Wellington
New Zealand; fax +64-4-4955014

Email: Jacek. KrawczykQvuw. ac. nz ;

http://www.vuw.ac.nz/~jacek

Version β.lb

Abstract-: A portfolio management problem is approximated as a Markov decision
chain. The weak Eulcr scheme is applied to discrétise the time evolution of a portfolio
and an inverse distance method is used to describe the transition probabilities.
The approximating Markov decision problem is solved by value iteration. Numerical
solutions of varying degrees of accuracy to a few specific financial portfolio problems
arc obtained. A sample of a fund manager’s objective functions is analysed to toll
which of them generates an acceptable Valuc-at-Risk.

Keywords: Computational economics; portfolio management; approximating Markov
decision chains; weak Eulcr scheme.

JEL: C8, C63, D92, C87, Gll

AMS: 93E20, 93E25, 90C39, 90C40, 90A09

1. INTRODUCTION

The purpose of this paper is to describe a numeri-
cal method capable of solving a class of stochastic
optimal control problems, which includes portfolio
management. The paper draws the idea of solving
a continuous finite-horizon stochastic optimal con-
trol problem as a Markov decision chain from [7]
and [6]. In this paper, the weakly consistent Eulcr
discretisation scheme, used for the approximation


of the stochastic process, and a scaling in the
policy space have greatly improved the solutions,
relative to those reported previously.

Optimal portfolio management can be modelled
as a stochastic optimal control problem. One can
usually solve a problem of this class by solving the
Hamilton-Jacobi-Bcllnian
(HJB) equation. This
is a complex procedure in any case. Often this
equation analytically insoluble and a numerical


* Research supported by VUW GSBGM and IGC. Helpful
comments by my colleagues: Graeme Guthrie, Martin
Lally and Leigh Roberts are gratefully acknowledged; all
remaining errors are mine.



More intriguing information

1. Personal Income Tax Elasticity in Turkey: 1975-2005
2. Studies on association of arbuscular mycorrhizal fungi with gluconacetobacter diazotrophicus and its effect on improvement of sorghum bicolor (L.)
3. The name is absent
4. Retirement and the Poverty of the Elderly in Portugal
5. The name is absent
6. The name is absent
7. The name is absent
8. Knowledge and Learning in Complex Urban Renewal Projects; Towards a Process Design
9. Strengthening civil society from the outside? Donor driven consultation and participation processes in Poverty Reduction Strategies (PRSP): the Bolivian case
10. Government spending composition, technical change and wage inequality
11. Popular Conceptions of Nationhood in Old and New European
12. Do the Largest Firms Grow the Fastest? The Case of U.S. Dairies
13. O funcionalismo de Sellars: uma pesquisa histδrica
14. The name is absent
15. Secondary stress in Brazilian Portuguese: the interplay between production and perception studies
16. Regional specialisation in a transition country - Hungary
17. The name is absent
18. The name is absent
19. Økonomisk teorihistorie - Overflødig information eller brugbar ballast?
20. The Institutional Determinants of Bilateral Trade Patterns