A remark on the set of arbitrage-free prices in a multi-period model

Abhishek Ranjan

A remark on the set of arbitrage-free prices in a multi-period model

Abhishek Ranjan

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Abstract

We study the convexity property of the set Q_F of arbitrage ‐ free prices of a multi
‐period financial structure F. The set of arbitrage‐free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short ‐ lived assets. Furthermore, we provide examples of equivalent financial structures F and F¹such that Q_Fis a convex cone, but Q_Fis neither convex nor a cone.

Original language	English
Journal	International Journal of Economic Theory
Volume	9
Pages (from-to)	35-43
ISSN	1742-7355
Publication status	Published - 2013

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abstract = "We study the convexity property of the set QF of arbitrage ‐ free prices of a multi‐period financial structure F. The set of arbitrage‐free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short ‐ lived assets. Furthermore, we provide examples of equivalent financial structures F and F1 such that QF is a convex cone, but QF is neither convex nor a cone.",

author = "Abhishek Ranjan",

year = "2013",

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journal = "International Journal of Economic Theory",

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T1 - A remark on the set of arbitrage-free prices in a multi-period model

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N2 - We study the convexity property of the set QF of arbitrage ‐ free prices of a multi‐period financial structure F. The set of arbitrage‐free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short ‐ lived assets. Furthermore, we provide examples of equivalent financial structures F and F1 such that QF is a convex cone, but QF is neither convex nor a cone.

AB - We study the convexity property of the set QF of arbitrage ‐ free prices of a multi‐period financial structure F. The set of arbitrage‐free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short ‐ lived assets. Furthermore, we provide examples of equivalent financial structures F and F1 such that QF is a convex cone, but QF is neither convex nor a cone.

M3 - Journal article

VL - 9

SP - 35

EP - 43

JO - International Journal of Economic Theory

JF - International Journal of Economic Theory

SN - 1742-7355

ER -