Representation of Square Integrable Martingales

Gopinath Kallianpur and Rajeeva L. Karandikar
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Gopinath Kallianpur: University of North Carolina, Department of Statistics
Rajeeva L. Karandikar: Indian Statistical Institute, Department of Mathematics & Statistics

Chapter 3 in Introduction to Option Pricing Theory, 2000, pp 71-78 from Springer

Abstract: Abstract In the last chapter, we saw that if M ∈ M2, then the indefinite stochastic integral Y t := ∫ 0 t f d M is a square integrable martingale. Can every L2-martingale on (Ω, F, (Ft), P) be expressed as a stochastic integral with respect to M? We can also pose the question another way. Can any square integrable functional on (Ω, FT, P) be represented as a stochastic integral? The present chapter will be devoted to this question.

Keywords: Option Price; Wiener Process; Local Martingale; Predictable Process; Wiener Space (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0511-1_3

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DOI: 10.1007/978-1-4612-0511-1_3

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