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Results on numerics for FBSDE with drivers of quadratic growth

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  • Peter Imkeller
  • Gon\c{c}alo dos Reis
  • Jianing Zhang
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    Abstract

    We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence of numerical approximation schemes for such systems of stochastic equations, path regularity of the solution processes is instrumental. We present a method based on the truncation of the driver, and explicitly exhibit error estimates as functions of the truncation height. We discuss a reduction method to FBSDE with globally Lipschitz continuous drivers, by using the Cole-Hopf exponential transformation. We finally illustrate our numerical approximation methods by giving simulations for prices and optimal hedges of simple insurance derivatives.

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    File URL: http://arxiv.org/pdf/1004.2248
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    Paper provided by arXiv.org in its series Papers with number 1004.2248.

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    Date of creation: Apr 2010
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    Handle: RePEc:arx:papers:1004.2248

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    Web page: http://arxiv.org/

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    Cited by:
    1. Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2011. "Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization," Economics Papers from University Paris Dauphine 123456789/7101, Paris Dauphine University.

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