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Optimal exponential utility in a jump bond market

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2010

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Xiong, Dewen

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-129303
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https://doi.org/10.1080/07362994.2011.532025
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Stochastic Analysis and Applications. 2010, 29(1), pp. 78-105. ISSN 0736-2994. Available under: doi: 10.1080/07362994.2011.532025

Zusammenfassung

We consider the optimal exponential utility in a bond market with jumps basing on a model similar to Bjork et al. [4], which is arbitrage free. Similar to the normalized integral with respect to the cylindrical martingale first introduced in Mikulevicius and Rozovskii [13], we introduce the (, Q0)-normalized martingale and local (, Q0)-normalized martingale. For a given maturity T0 ∈ [0, T*], we describe the minimal entropy martingale (MEM) based on [T0, T*] by a backward semimartingale equation (BSE) w.r.t. the (, Q0)-normalized martingale. Then we give an explicit form of the optimal approximate wealth to the optimal exp-utility problem by making use of the solution of the BSE. Finally, we describe the dynamics of the exp utility indifference valuation of a bounded contingent claim H ∈ L∞(FT0) by another BSE under the minimal entropy martingale measure in the incomplete market.

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510 Mathematik

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ISO 690XIONG, Dewen, Michael KOHLMANN, 2010. Optimal exponential utility in a jump bond market. In: Stochastic Analysis and Applications. 2010, 29(1), pp. 78-105. ISSN 0736-2994. Available under: doi: 10.1080/07362994.2011.532025
BibTex
@article{Xiong2010Optim-832,
  year={2010},
  doi={10.1080/07362994.2011.532025},
  title={Optimal exponential utility in a jump bond market},
  number={1},
  volume={29},
  issn={0736-2994},
  journal={Stochastic Analysis and Applications},
  pages={78--105},
  author={Xiong, Dewen and Kohlmann, Michael}
}
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    <dcterms:abstract xml:lang="eng">We consider the optimal exponential utility in a bond market with jumps basing on a model similar to Bjork et al. [4], which is arbitrage free. Similar to the normalized integral with respect to the cylindrical martingale first introduced in Mikulevicius and Rozovskii [13], we introduce the (, Q0)-normalized martingale and local (, Q0)-normalized martingale. For a given maturity T0 ∈ [0, T*], we describe the minimal entropy martingale (MEM) based on [T0, T*] by a backward semimartingale equation (BSE) w.r.t. the (, Q0)-normalized martingale. Then we give an explicit form of the optimal approximate wealth to the optimal exp-utility problem by making use of the solution of the BSE. Finally, we describe the dynamics of the exp utility indifference valuation of a bounded contingent claim H ∈ L∞(FT0) by another BSE under the minimal entropy martingale measure in the incomplete market.</dcterms:abstract>
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