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REPRESENTING MARTINGALE MEASURES WHEN ASSET PRICES ARE CONTINUOUS AND BOUNDED

REPRESENTING MARTINGALE MEASURES WHEN ASSET PRICES ARE CONTINUOUS AND BOUNDED Department of Mathematics, Institute of Actuarial Sciences, Vrije Universiteit Brussel, 8-1050 Brussel, Belgium 1 . INTRODUCTION In their fundamental paper, Harrison and Kreps ( 1979) introduced the concept of equivalent martingale measures. Absence of arbitrage alone was not sufficient to obtain an equivalent martingale measure for the stochastic processes describing asset prices. It turned out that a topological condition was needed. In Harrison and Kreps (1979) the concept of viability, having a direct economic interpretation, was introduced and used to provide the topological condition needed to apply the Hahn-Banach theorem. Different solutions have been introduced to relate the topological conditions more closely to the concept of absence of arbitrage profits; see Harrison and Pliska (1981), Back and Pliska (1991), Dalang, Morton, and Willinger (1989), and Duffie and Huang (1986). In Stricker (1990) the problem was solved by using the theory of stochastic integration and a HahnBanach-like theorem of Yan. The absence of arbitrage was made more restrictive because trading of nonelementary strategies was allowed. Stricker was able to solve the problem for asset prices which are in LP, where 1 2 p < m . The case p = x remained unsolved. In this paper we solve this http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Finance Wiley

REPRESENTING MARTINGALE MEASURES WHEN ASSET PRICES ARE CONTINUOUS AND BOUNDED

Mathematical Finance , Volume 2 (2) – Apr 1, 1992

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References (10)

Publisher
Wiley
Copyright
Copyright © 1992 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0960-1627
eISSN
1467-9965
DOI
10.1111/j.1467-9965.1992.tb00041.x
Publisher site
See Article on Publisher Site

Abstract

Department of Mathematics, Institute of Actuarial Sciences, Vrije Universiteit Brussel, 8-1050 Brussel, Belgium 1 . INTRODUCTION In their fundamental paper, Harrison and Kreps ( 1979) introduced the concept of equivalent martingale measures. Absence of arbitrage alone was not sufficient to obtain an equivalent martingale measure for the stochastic processes describing asset prices. It turned out that a topological condition was needed. In Harrison and Kreps (1979) the concept of viability, having a direct economic interpretation, was introduced and used to provide the topological condition needed to apply the Hahn-Banach theorem. Different solutions have been introduced to relate the topological conditions more closely to the concept of absence of arbitrage profits; see Harrison and Pliska (1981), Back and Pliska (1991), Dalang, Morton, and Willinger (1989), and Duffie and Huang (1986). In Stricker (1990) the problem was solved by using the theory of stochastic integration and a HahnBanach-like theorem of Yan. The absence of arbitrage was made more restrictive because trading of nonelementary strategies was allowed. Stricker was able to solve the problem for asset prices which are in LP, where 1 2 p < m . The case p = x remained unsolved. In this paper we solve this

Journal

Mathematical FinanceWiley

Published: Apr 1, 1992

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