Sampled Control for Mean-Variance Hedging in a Jump Diffusion Financial Market

Author

Costa, O.L.V. ; Maiali, A.C. ; Pinto, Afonso DeC

Author_Institution

Depto. Eng. Telecomun. e Controle, Univ. de Sao Paulo, Sao Paulo, Brazil

Volume

55

Issue

7

fYear

2010

fDate

7/1/2010 12:00:00 AM

Firstpage

1704

Lastpage

1709

Abstract

In this technical note we consider the mean-variance hedging problem of a jump diffusion continuous state space financial model with the re-balancing strategies for the hedging portfolio taken at discrete times, a situation that more closely reflects real market conditions. A direct expression based on some change of measures, not depending on any recursions, is derived for the optimal hedging strategy as well as for the “fair hedging price” considering any given payoff. For the case of a European call option these expressions can be evaluated in a closed form.

Keywords

continuous systems; investment; state-space methods; stock markets; European call option; continuous state space financial model; hedging portfolio; jump diffusion financial market; mean-variance hedging; sampled control; Analysis of variance; Brazil Council; Dynamic programming; Economic indicators; Investments; Optimal control; Portfolios; Pricing; State-space methods; Stochastic processes; Tree data structures; Discrete-time mean-variance hedging; optimal control; options pricing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2046923

Filename

5440959