Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-04-08
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semiexplicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes.
Analytical and numerical examples are both presented to illustrate the effectiveness of our optimal strategy.
Our study establishes the connection between our financial system and existing general semimartingale based discussions by justifying required conditions.
More precisely, there are three steps involved.
First, we firmly prove the no-arbitrage condition to be true for our financial market, which is used as an assumption in existing discussions.
In doing so, we explicitly construct the square-integrable density process of the variance-optimal martingalemeasure (VOMM).
Second, we derive a backward stochastic differential equation (BSDE) with jumps for the mean-value process of a given contingent claim.
The unique existence of adapted strong solution tothe BSDE is proved under suitable terminal conditions including both European call and put options as special cases.
Third, by combining the solution of the BSDE and the VOMM, we reach the justification ofthe global risk optimality for our hedging strategy.
American Psychological Association (APA)
Dai, Wanyang. 2015. Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-20.
https://search.emarefa.net/detail/BIM-1074317
Modern Language Association (MLA)
Dai, Wanyang. Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes. Mathematical Problems in Engineering No. 2015 (2015), pp.1-20.
https://search.emarefa.net/detail/BIM-1074317
American Medical Association (AMA)
Dai, Wanyang. Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-20.
https://search.emarefa.net/detail/BIM-1074317
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074317