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Weak convergence of semimartingales and discretisation methods

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  • Platen, Eckhard
  • Rebolledo, Rolando

Abstract

Given a semimartingale one can construct a system ([lambda], A, B, C) where [lambda] is the distribution of the initial value and (A, B, C) is the triple of global characteristics. Thus, given a process X and a system ([lambda], A, B, C) one can look for all probability measures P such that X is a P-semimartingale with initial distribution [lambda] and global characteristics (A, B, C). We say that such a measure P is a solution to the semimartingale problem ([lambda], A, B, C). The paper is devoted to the study of a special type of semimartingale problem. We look for sufficient conditions to insure the existence of solutions and we develop a method to construct them by means of time-discretised schemes, using weak topology for probability measures.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 20 (1985)
Issue (Month): 1 (July)
Pages: 41-58

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Handle: RePEc:eee:spapps:v:20:y:1985:i:1:p:41-58

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Related research

Keywords: semimartingale problems weak topologies time-discretised schemes domain of attraction stability of discretised schemes;

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Cited by:
  1. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1.
  2. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  3. Jeremy Graveline & Irina Zviadadze & Mikhail Chernov, 2012. "Crash Risk in Currency Returns," 2012 Meeting Papers 753, Society for Economic Dynamics.

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