title: Stochastic mesh method for optimal stopping problems
metadata.name: dc.contributor.author
metadata.value: Kashtanov, Yuriy N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Fedyaev, Igor P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-09-10T13:44:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T13:44:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kashtanov Yu. N., Fedyaev I. P. Stochastic mesh method for optimal stopping problems. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 425–434.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.306
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19393
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The stochastic mesh method for solving a multidimensional optimal stopping problem for
  a diffusion process with non-linear payoff is considered. To solve the problem in the case
  of payoff for an Asian option with geometric average we provide a special discretization
  scheme for the diffusion process. This sampling scheme allows one to get rid of singularities
  in transition probabilities. Then, we consider transition probabilities of a stochastic mesh
  defined as averaged densities. Two estimates of the solution to the problem by the stochastic
  mesh method are given. The consistency of the defined estimates is proved. It is shown that
  the variance of the solution estimates is inversely proportional to the number of points in
  each mesh layer. The result extends the application area of the stochastic mesh method.
  A numerical example of the result is presented. We applying estimates to the call and put
  options compared to the option prices obtained through the regular mesh.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This study was supported by the Russian Foundation for Basic Research, projects No 17-01-00267 and 20-01-00011.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: optimal stopping
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stochastic mesh
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Asian option with geometric average
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stochastic mesh method for optimal stopping problems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 425-434.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19393/1/425-434.pdf
resources.format: Adobe PDF
resources.size: 304,8 kB