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An Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems

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Author Info
Denis Belomestny
Pavel V. Gapeev
Abstract

A new algorithm for finding value functions of finite horizon optimal stopping problems in one-dimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation converges in a finite number of steps and delivers in each step a lower or an upper bound for value of discretized problem on the whole time interval. The remarks on the application of the method for solving integral equations related to some optimal stopping problems are given.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-043.pdf
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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-043.

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Length: 18 pages
Date of creation: May 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-043

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Related research
Keywords: Optimal stopping finite horizon diffusion process upper and lower bounds Black-Scholes model American put option Asian option Russian option Bayesian sequential testing problem disorder detection problem

Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

This paper has been announced in the following NEP Reports:

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  1. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 547-72. [Downloadable!] (restricted)
  2. Alexander Novikov & Albert Shiryaev, 2004. "On an Effective Solution of the Optimal Stopping Problem for Random Walks," Research Paper Series 131, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  3. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 597-626.
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