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

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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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  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Yushi Hamaguchi

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  1. Yushi Hamaguchi
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Correspondence to Yushi Hamaguchi.

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This work was supported by JSPS KAKENHI Grant Number JP18J20973.

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Hamaguchi, Y. BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets. Japan J. Indust. Appl. Math. 38, 425–453 (2021). https://doi.org/10.1007/s13160-020-00442-y

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  • DOI: https://doi.org/10.1007/s13160-020-00442-y

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