Skip to main content
Article thumbnail
Location of Repository

An Optimization Approach to Weak Approximation of Lévy-Driven Stochastic Differential Equations

By Kenji Kashima and Reiichiro Kawai

Abstract

This is the authors' final draft of the paper published as Lecture Notes in Control and Information Sciences, 2010, 398, pp. 263-272. The original publication is available at www.springerlink.com. Doi: 10.1007/978-3-540-93918-4We propose an optimization approach to weak approximation of Lévy-driven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Lévy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We also investigate methods for approximation at some different intermediate time points simultaneously

Publisher: Springer Verlag
Year: 2010
DOI identifier: 10.1007/978-3-540-93918-4
OAI identifier: oai:lra.le.ac.uk:2381/8091
Journal:

Suggested articles

Citations

  1. (2008). A method of moments approach to pricing double barrier contracts driven by a general class of jump diffusions, available at arXiv:0812.4548v1.
  2. (2009). A weak approximation of stochastic differential equations with jumps through tempered polynomial programming, doi
  3. (2001). Computing moments of the exit time distribution for Markov processes by linear programming, doi
  4. (1999). Le´vy processes and infinitely divisible distributions, doi
  5. (2004). Le´vy Processes and Stochastic Calculus, doi
  6. (2000). Moment problems and semidefinite programming, In: Handbook on semidefinite programming: Theory, Algorithms, doi
  7. (1999). Numerical Solution of Stochastic Differential Equations, Third Printing, doi
  8. (2008). Optimization based option pricing bounds via piecewise polynomial super- and sub-martingales, In: doi
  9. (2006). Pricing a class of exotic via moments and SDP relaxations, doi
  10. (2004). SDP vs. LP relaxations for the moment approach in some performance evaluation problems, Stochastic Models, doi
  11. (2006). SeDuMi version 1.1.
  12. (2003). Semidefinite programming relaxations for semialgebraic problems, doi
  13. (2004). SOS-TOOLS: Sum of squares optimization toolbox for MATLAB.
  14. (1997). The Euler scheme for Le´vy driven stochastic differential equations, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.