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Path regularity and explicit convergence rate for BSDE with truncated quadratic growth

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  • Imkeller, Peter
  • Dos Reis, Gonçalo

Abstract

We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the solution processes of the qgBSDE, in particular we prove an extension of Zhang's path regularity theorem to the quadratic growth setting. We give explicit convergence rates for the difference between the solution of a qgBSDE and its truncation, filling an important gap in numerics for qgBSDE. We give an alternative proof of second order Malliavin differentiability for BSDE with drivers that are Lipschitz continuous (and differentiable), and then derive an analogous result for qgBSDE.

Suggested Citation

  • Imkeller, Peter & Dos Reis, Gonçalo, 2010. "Path regularity and explicit convergence rate for BSDE with truncated quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 348-379, March.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:3:p:348-379
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    References listed on IDEAS

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    1. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    2. 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.
    3. Briand, Philippe & Confortola, Fulvia, 2008. "BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 818-838, May.
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    Cited by:

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    2. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    3. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2020. "An implicit numerical scheme for a class of backward doubly stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3295-3324.
    4. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    5. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
    6. Dirk Becherer & Plamen Turkedjiev, 2014. "Multilevel approximation of backward stochastic differential equations," Papers 1412.3140, arXiv.org.
    7. dos Reis, Gonçalo & Réveillac, Anthony & Zhang, Jianing, 2011. "FBSDEs with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2114-2150, September.
    8. Santiago Moreno-Bromberg & Traian Pirvu & Anthony R'eveillac, 2011. "CRRA Utility Maximization under Risk Constraints," Papers 1106.1702, arXiv.org, revised Mar 2012.
    9. Chaudru de Raynal, P.E. & Garcia Trillos, C.A., 2015. "A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2206-2255.
    10. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.

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