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The Dynamic q-Valuation of a Contingent Claim in a Continuous Market Model

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2009

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Xiong, Dewen

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-86302
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https://doi.org/10.1080/07362990802564814
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Stochastic Analysis and Applications. 2009, 27(1), pp. 95-124. Available under: doi: 10.1080/07362990802564814

Zusammenfassung

In this article, we consider a new valuation, which we call dynamic q-valuation C~qt(B) of a contingent claim in a semimartingale model with a general continuous filtration. We prove that this valuation has the properties of a convex risk valuation and by making use of the (p, B)-optimal martingale measure introduced in Mania et al. we obtain a backward semimartingale equation (BSE) to characterize the dynamic q-valuation. We prove the convexity of this q-valuation its time-consistency property. Given q and ^q, we consider the ∈ f-convolution of C~q(B) and C~^q(B). This new risk valuation is shown to have an explicitly stated representation as a backward semimartingale equation (BSE). Furthermore, we discuss the convergence of a sequence of ∈ f-valuation of C~q(B). So, starting from the q-valuation we derive several new risk-measures which allow for an explicit representation.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Backward semimartingale equation (BSE), Convex risk valuation, p-optimal martingale measure, q-valuation

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ISO 690KOHLMANN, Michael, Dewen XIONG, 2009. The Dynamic q-Valuation of a Contingent Claim in a Continuous Market Model. In: Stochastic Analysis and Applications. 2009, 27(1), pp. 95-124. Available under: doi: 10.1080/07362990802564814
BibTex
@article{Kohlmann2009Dynam-781,
  year={2009},
  doi={10.1080/07362990802564814},
  title={The Dynamic q-Valuation of a Contingent Claim in a Continuous Market Model},
  number={1},
  volume={27},
  journal={Stochastic Analysis and Applications},
  pages={95--124},
  author={Kohlmann, Michael and Xiong, Dewen}
}
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    <dcterms:abstract xml:lang="eng">In this article, we consider a new valuation, which we call dynamic q-valuation C~qt(B) of a contingent claim in a semimartingale model with a general continuous filtration. We prove that this valuation has the properties of a convex risk valuation and by making use of the (p, B)-optimal martingale measure introduced in Mania et al. we obtain a backward semimartingale equation (BSE) to characterize the dynamic q-valuation. We prove the convexity of this q-valuation its time-consistency property. Given q and ^q, we consider the ∈ f-convolution of C~q(B) and C~^q(B). This new risk valuation is shown to have an explicitly stated representation as a backward semimartingale equation (BSE). Furthermore, we discuss the convergence of a sequence of ∈ f-valuation of C~q(B). So, starting from the q-valuation we derive several new risk-measures which allow for an explicit representation.</dcterms:abstract>
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