On an optimization problem related to static super-replicating strategies

Xinliang Chen; Griselda Deelstra; Jan Dhaene; Daniël Linders; Michèle Vanmaele

doi:10.1016/j.cam.2014.10.003

On an optimization problem related to static super-replicating strategies

Xinliang Chen, Griselda Deelstra, Jan Dhaene, Daniël Linders, Michèle Vanmaele

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.

Original language	English (US)
Pages (from-to)	213-230
Number of pages	18
Journal	Journal of Computational and Applied Mathematics
Volume	278
DOIs	https://doi.org/10.1016/j.cam.2014.10.003
State	Published - Apr 15 2015
Externally published	Yes

Keywords

Asian options
Basket options
Comonotonicity
Super-hedging strategies

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Online availability

10.1016/j.cam.2014.10.003

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title = "On an optimization problem related to static super-replicating strategies",

abstract = "In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.",

keywords = "Asian options, Basket options, Comonotonicity, Super-hedging strategies",

author = "Xinliang Chen and Griselda Deelstra and Jan Dhaene and Dani{\"e}l Linders and Mich{\`e}le Vanmaele",

note = "Funding Information: Jan Dhaene and Dani{\"e}l Linders acknowledge the financial support of the Onderzoeksfonds KU Leuven ( GOA/12/002/TBA and GOA/13/002 ). Xin-liang Chen acknowledges the financial support of the Onderzoeksfonds KU Leuven ( GOA/07 ) in his Ph.D. period. Griselda Deelstra acknowledges support of the ARC grant IAPAS “Interaction between analysis, probability and actuarial sciences”, 2012–2017. Publisher Copyright: {\textcopyright} 2014 Elsevier B.V. All rights reserved.",

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AU - Chen, Xinliang

AU - Deelstra, Griselda

AU - Dhaene, Jan

AU - Linders, Daniël

AU - Vanmaele, Michèle

N1 - Funding Information: Jan Dhaene and Daniël Linders acknowledge the financial support of the Onderzoeksfonds KU Leuven ( GOA/12/002/TBA and GOA/13/002 ). Xin-liang Chen acknowledges the financial support of the Onderzoeksfonds KU Leuven ( GOA/07 ) in his Ph.D. period. Griselda Deelstra acknowledges support of the ARC grant IAPAS “Interaction between analysis, probability and actuarial sciences”, 2012–2017. Publisher Copyright: © 2014 Elsevier B.V. All rights reserved.

PY - 2015/4/15

Y1 - 2015/4/15

N2 - In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.

AB - In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.

KW - Asian options

KW - Basket options

KW - Comonotonicity

KW - Super-hedging strategies

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EP - 230

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

On an optimization problem related to static super-replicating strategies

Abstract

Keywords

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