Stochastic mesh method for optimal stopping problems
-
Yuri Kashtanov
Abstract
A Monte Carlo method for solving the multi-dimensional optimal stopping problem is considered. Consistent estimators for a general jump-diffusion are pointed out. It is shown that the variance of estimators is inverse proportional to the number of points in each layer of the mesh.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 17-01-00267
Funding statement: This work was supported by RFBR grant 17-01-00267.
References
[1] A. Avramidis and H. Matzinger, Convergence of the stochastic mesh estimator for pricing Bermudan options, J. Comput. Finance 7 (2004), 73–91. 10.21314/JCF.2004.118Search in Google Scholar
[2] V. Bally, L. Caramellino and A. Zanette, Pricing and hedging American options by Monte Carlo methods using a Malliavin calculus approach, J. Monte Carlo Methods Appl. 11 (2005), 97–134. 10.1515/156939605777585944Search in Google Scholar
[3] M. Broadie and P. Glasserman, A stochastic mesh method for pricing high-dimensional American options, J. Comput. Finance 7 (2004), 35–72. 10.21314/JCF.2004.117Search in Google Scholar
[4] Y. Kashtanov, Financial Mathematics Models and Statistical Simulation, VVM, Saint Petersburg, 2013. Search in Google Scholar
[5] Y. Kashtanov, Consistency of the stochastic mesh method, The Sixth International Conference on Advances in System Simulation, Saint Petersburg State University, Saint Petersburg (2014), 103–107. Search in Google Scholar
[6] B. Øksendal and A. Sulem, Applied Stochastic Control of Jump Diffusion, Springer, Berlin, 2007. 10.1007/978-3-540-69826-5Search in Google Scholar
[7] A. N. Shiryaev, Optimal Stopping Rules, Springer, Berlin, 2008. Search in Google Scholar
[8]
B. von Bahr and C.-G. Esseen,
Inequalities for the rth absolute moment of a some of random variables,
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Invariant density estimation for a reflected diffusion using an Euler scheme
- Feistel-inspired scrambling improves the quality of linear congruential generators
- Stochastic polynomial chaos expansion method for random Darcy equation
- Effect of covariate misspecifications in the marginalized zero-inflated Poisson model
- Stochastic mesh method for optimal stopping problems
- Computing with bivariate COM-Poisson model under different copulas
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
Articles in the same Issue
- Frontmatter
- Invariant density estimation for a reflected diffusion using an Euler scheme
- Feistel-inspired scrambling improves the quality of linear congruential generators
- Stochastic polynomial chaos expansion method for random Darcy equation
- Effect of covariate misspecifications in the marginalized zero-inflated Poisson model
- Stochastic mesh method for optimal stopping problems
- Computing with bivariate COM-Poisson model under different copulas
- Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher
