nach oben

Journal of Scientific Computing

Erschienen in:

27.04.2016

Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps

verfasst von: Yu Fu, Weidong Zhao, Tao Zhou

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this work, we are concerned with multistep schemes for solving forward backward stochastic differential equations with jumps. The proposed multistep schemes admit many advantages. First of all, motivated by the local property of jump diffusion processes, the Euler method is used to solve the associated forward stochastic differential equation with jump, which reduce dramatically the entire computational complexity, however, the quantities of interests in the backward stochastic differential equations (with jump) are still of high order rate of convergence. Secondly, in each time step, only one jump is involved in the computational procedure, which again reduces dramatically the computational complexity. Finally, the method applies easily to partial-integral differential equations (and some nonlocal PDE models), by using the generalized Feynman–Kac formula. Several numerical experiments are presented to demonstrate the effectiveness of the proposed multistep schemes.

Vorheriger Artikel An Algorithmic Exploration of the Existence of High-Order Summation by Parts Operators with Diagonal Norm

Nächster Artikel The Jacobi Collocation Method for a Class of Nonlinear Volterra Integral Equations with Weakly Singular Kernel

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Barles, G., Buckdahn, R., Pardoux, E.: Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60, 57–83 (1997)MathSciNetCrossRefMATH

Becherer, D.: Bounded solution to BSDE’s with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 16, 2027–2054 (2006)MathSciNetCrossRefMATH

Bender, C., Zhang, J.: Time discretization and markovian iteration for coupled FBSDEs. Ann. Appl. Probab. 18, 143–177 (2008)MathSciNetCrossRefMATH

Bouchard, B., Elie, R.: Discrete time approximation of decoupled forward–backward SDE with jumps. Stoch. Process. Appl. 118, 53–75 (2008)MathSciNetCrossRefMATH

Cont, R., Tankov, R.: Financial modelling with jumpe processes. Chapman and Hall/CRC Press, London (2004)MATH

Delong, L.: Backward stochastic differential equations with jumps and their actuarial and financial applications. BSDEs with jumps. Springer, New York (2013)CrossRefMATH

Du, Q., Gunzburger, M., Lebourq, R., Zhou, K.: Analysis and approximation of nonlocal diffusion problems with volume constraints. SIAM Rev. 4, 667–696 (2012)MathSciNetCrossRefMATH

Fu, Y., Yang, J., Zhao, W.: Prediction-correction scheme for decoupled forward backward stochastic differential equations with jumps. submitted (2015)

Fu, Y., Zhao, W.: An explicit second-order numerical scheme to solve decoupled forward backward stochastic equations. East Asian J. Appl. Math. 4, 368–385 (2014)MathSciNetMATH

10.

Kong, T., Zhao, W., Zhou, T.: High order numerical schemes for second order FBSDEs with applications to stochastic optimal control. arXiv:1502.03206 (2015)

11.

Lemor, J.P., Gobet, E., Warin, X.: A regression-based monte carlo method for backward stochastic differential equations. Ann. Appl. Probab. 15(3), 2172–2202 (2005)

12.

Li, J., Peng, S.: Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of hamilton–jacobi–bellman equations. Nonlinear Anal. Theory Methods Appl. 70, 1776–1796 (2009)MathSciNetCrossRefMATH

13.

Milstein, G.N., Tretyakov, M.V.: Numerical algorithms for forward–backward stochastic differential equations. SIAM J. Sci. Comput. 28, 561–582 (2006)MathSciNetCrossRefMATH

14.

Morlais, M.: A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem. Stoch. Process. Appl. 120, 1966–1996 (2010)MathSciNetCrossRefMATH

15.

Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14, 56–61 (1990)MathSciNetCrossRefMATH

16.

Ruijter, M., Oosterlee, C.W.: A fourier cosine method for an efficient computation of solutions to BSDEs. SIAM J. Sci. Comput. 37(2), A859–A889 (2015)MathSciNetCrossRefMATH

17.

Tang, S., Li, X.: Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Sci. Comput. 32, 1447–1475 (1994)MathSciNetMATH

18.

Tang, T., Zhao, W., Zhou, T.: Highly accurate numerical schemes for forward backward stochastic differential equations based on deferred correction approach. submitted (2015)

19.

Yang, J., Zhao, W.: Convergence of recent multistep schemes for a forward–backward stochastic differential equation. East Asian J. Appl. Math. 5(4), 387–404 (2015)MathSciNetCrossRef

20.

Zhang, G., Zhao, W., Webster, C., Gunzburger, M.: Numerical solution of backward stochastic differential equations with jumps for a class of nonlocal diffusion problems. arXiv preprint arXiv:1503.00213 (2015)

21.

Zhao, W., Chen, L., Peng, S.: A new kind of accurate numerical method for backward stochastic differential equations. SIAM J. Sci. Comput. 28, 1563–1581 (2006)MathSciNetCrossRefMATH

22.

Zhao, W., Fu, Y., Zhou, T.: New kinds of high-order multistep schemes for coupled forward backward stochastic differential equations. SIAM J. Sci. Comput. 36, A1731–A1751 (2014)MathSciNetCrossRefMATH

23.

Zhao, W., Zhang, G., Ju, L.: A stable multistep scheme for solving backward stochastic differential equations. SIAM J. Numer. Anal. 48, 1369–1394 (2010)MathSciNetCrossRefMATH

24.

Zhao, W., Zhang, W., Zhang, G.: Numerical schemes for forward–backward stochastic differential equaiton to nonlinear partial integro-differential equations. submitted (2015)

Titel: Multistep Schemes for Forward Backward Stochastic Differential Equations with Jumps
verfasst von: Yu Fu
Weidong Zhao
Tao Zhou
Publikationsdatum: 27.04.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0212-y

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 2/2016

Krylov Integration Factor Method on Sparse Grids for High Spatial Dimension Convection–Diffusion Equations

Convergent Non-overlapping Domain Decomposition Methods for Variational Image Segmentation

An Algorithmic Exploration of the Existence of High-Order Summation by Parts Operators with Diagonal Norm

On Standard Finite Difference Discretizations of the Elliptic Monge–Ampère Equation

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements

Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials