# Mean Variance Hedging In A General Jump Market

## Author Info

• DEWEN XIONG

()

(Department of Mathematics, Shanghai Jiaotong University, Shanghai (200240), P. R. China)

• MICHAEL KOHLMANN

()

(Department of Mathematics and Statistics, University of Konstanz, D-78457, Konstanz, Germany)

Registered author(s):

## Abstract

We consider a financial market in which the discounted price process S is an ℝd-valued semimartingale with bounded jumps, and the variance-optimal martingale measure (VOMM) Qopt is only known to be a signed measure. We give a backward semimartingale equation (BSE) and show that the density process Zopt of Qopt with respect to P is a possibly non-positive stochastic exponential if and only if this BSE has a solution. For a general contingent claim H, we consider the following generalized version of the classical mean-variance hedging problem $$\min_{\pi\in Adm} E\{(X^{w,\pi}_{\tilde\tau})^2 I_{\{{\tilde\tau}\leq T\}}+|H - X^{w,\pi}_T|^2 I_{\{{\tilde\tau} > T\}}\},$$ where ${\tilde\tau} = \inf\{t > 0; Z^{\rm opt}_t=0\}$. We represent the optimal strategy and the optimal cost of the mean-variance hedging by means of another backward martingale equation (BME) and an appropriate predictable process δ both with a straightforward intuitive interpretation.

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## Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 13 (2010)
Issue (Month): 05 ()
Pages: 789-820

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 Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:05:p:789-820 Contact details of provider: Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml Order Information: Email:

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