An optimization approach to weak approximation of stochastic differential equations with jumps

DOI10.1016/j.apnum.2010.10.012zbMath1210.65012OpenAlexW2063665381MaRDI QIDQ631923

Kenji Kashima, Reiichiro Kawai

Publication date: 14 March 2011

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2381/9044

zbMATH Keywords

numerical resultsLévy processesstochastic differential equationsweak approximationpolynomial programmingOrnstein-Uhlenbeck-type processDoléans-Dade stochastic exponentialtruncated stable process

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Uses Software

• Sostools
• SeDuMi

Cites Work

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• On layered stable processes
• Tempering stable processes
• Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
• Strong approximations of stochastic differential equations with jumps
• A survey of numerical methods for stochastic differential equations
• Stochastic differential equations with jumps
• The Euler scheme for Lévy driven stochastic differential equations
• Semidefinite programming relaxations for semialgebraic problems
• The approximate Euler method for Lévy driven stochastic differential equations
• Time Discrete Taylor Approximations for It?? Processes with Jump Component
• On simulation from infinitely divisible distributions
• Rate of Weak Convergence of the Euler Approximation for Diffusion Processes with Jumps
• Weak Approximations and Extrapolations of Stochastic Differential Equations with Jumps
• Lévy Processes and Stochastic Calculus
• PRICING A CLASS OF EXOTIC OPTIONS VIA MOMENTS AND SDP RELAXATIONS