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BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets

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  • Yushi Hamaguchi

Abstract

We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs and prove that the sequence of solutions of corresponding finite-dimensional BSDEs approximates the original solution. We also consider the hedging problem in bond markets and prove that, for an approximately attainable contingent claim, the sequence of locally risk-minimizing strategies based on small markets converges to the generalized hedging strategy.

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  • Yushi Hamaguchi, 2018. "BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets," Papers 1806.04025, arXiv.org.
    • Handle: RePEc:arx:papers:1806.04025
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    References listed on IDEAS

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    1. Marzia Donno & Maurizio Pratelli, 2004. "On the use of measure-valued strategies in bond markets," Finance and Stochastics, Springer, vol. 8(1), pages 87-109, January.
    2. M. De Donno & M. Pratelli, 2006. "A theory of stochastic integration for bond markets," Papers math/0602532, arXiv.org.
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    4. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    5. De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
    6. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
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