A splitting method for fully nonlinear degenerate parabolic PDEs

Electronic Journal of Probability

Volumn 18, Issue , 2013, Pages

  Tan, Xiaolu ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Nonlinear degenerate PDE; Numerical scheme; Splitting method; Viscosity solution

Indexed keywords

EID: 84873309955     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v18-1967     Document Type: Article

References (18)

1. Bardou, Olivier; Bouthemy, Sandrine; Pagès, Gilles. When are swing options bang-bang? Int. J. Theor. Appl. Finance 13 (2010), no. 6, 867-899. MR-2718983
2. Barles, Guy; Jakobsen, Espen R. Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations. Math. Comp., 76 (2007), no. 260, 1861-1893 (electronic). MR-2336272
3. Barles, G.; Souganidis, P. E. Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal. 4 (1991), no. 3, 271-283. MR-1115933
4. Bonnans, J. Frédéric; Ottenwaelter, élisabeth; Zidani, Housnaa. A fast algorithm for the two dimensional HJB equation of stochastic control. M2AN Math. Model. Numer. Anal. 38 (2004), no. 4, 723-735. MR-2087732
5. Bouchard, Bruno; Touzi, Nizar. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stochastic Process. Appl. 111 (2004), no. 2, 175-206. MR-2056536
6. B. Bouchard and X. Warin, Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods, preprint, 2011.
7. J.F. Bonnans, Z. Cen and T. Christel, Energy contracts management by stochastic programming techniques, to appear in special issue of "Annals of Operations Research" on "stochastic programming".
8. Z. Chen and P.A. Forsyth, A Semi-Lagrangian Approach for Natural Gas Storage Valuation and Optimal Operation SIAM J. Scientific Computing 30 (2007), 339-368.
9. Cheridito, Patrick; Soner, H. Mete; Touzi, Nizar; Victoir, Nicolas. Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs. Comm. Pure Appl. Math. 60 (2007), no. 7, 1081-1110. MR-2319056
10. D. Crisan, and K. Manolarakis, Solving Backward Stochastic Differential Equations using the Cubature Method, preprint, 2011.
11. Dai, Min; Kwok, Yue Kuen; Zong, Jianping. Guaranteed minimum withdrawal benefit in variable annuities. Math. Finance 18 (2008), no. 4, 595-611. MR-2454673
12. K. Debrabant and E.R. Jakobsen, Semi-Lagrangian schemes for linear and fully nonlinear diffusion equations, preprint, 2009.
13. Fahim, Arash; Touzi, Nizar; Warin, Xavier. A probabilistic numerical method for fully nonlinear parabolic PDEs. Ann. Appl. Probab. 21 (2011), no. 4, 1322-1364. MR-2857450
14. Gobet, Emmanuel; Lemor, Jean-Philippe; Warin, Xavier. A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann. Appl. Probab. 15 (2005), no. 3, 2172-2202. MR-2152657
15. F.A. Longstaff and R.S. Schwartz, Valuing American options by simulation: a simple leastsquare approach, Review of Finnaical studies, 14 (2001), 113-147.
16. A. Porchet, Problems of Valuation and Organization in Energy Markets, PhD Dissertation, Universitl e{ogonek} Paris Dauphine, 2008.
17. Rogers, L. C. G.; Shi, Z. The value of an Asian option. J. Appl. Probab. 32 (1995), no. 4, 1077-1088. MR-1363350
18. H.M. Soner, N. Touzi and J. Zhang, Wellposedness of second order backward SDEs, Probability Theory and Related Fields, to appear.