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MEAN VARIANCE HEDGING IN A GENERAL JUMP MARKET
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 Z...
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Published in: | International journal of theoretical and applied finance 2010-08, Vol.13 (5), p.789-820 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | 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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ISSN: | 0219-0249 1793-6322 |
DOI: | 10.1142/S0219024910006005 |