Local Martingales and the Fundamental Asset Pricing Theorems in the Discrete-Time Case

Posted: 16 Jul 1998

See all articles by Jean Jacod

Jean Jacod

Université Paris VI Pierre et Marie Curie

A.N. Shiryaev

Steklov Mathematical Institute

Abstract

This paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in discrete-time and finite horizon: namely the no-arbitrage theorem, and the market completeness theorem. Some elementary but apparently new results are also given on discrete-time martingale theory, and in particular a new condition for a local martingale to be a martingale.

JEL Classification: G12

Suggested Citation

Jacod, Jean and Shiryaev, A.N., Local Martingales and the Fundamental Asset Pricing Theorems in the Discrete-Time Case. Finance And Stochastics, Vol. 2, Issue 3, 1998. Available at SSRN: https://ssrn.com/abstract=108008

Jean Jacod (Contact Author)

Université Paris VI Pierre et Marie Curie ( email )

4, Place Jussieu, B.P. 169
Laboratoire de Probabilites
F-75252-Paris Cedex 05
France
01 44 27 53 21 (Phone)

A.N. Shiryaev

Steklov Mathematical Institute ( email )

Gubkina St. 8
Moscow, 117966

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