Continuous financial models

Peter Carr, Qiji Jim Zhu

Research output: Chapter in Book/Report/Conference proceedingChapter


We turn to discuss continuous financial models. These models in general involve infinite dimensional spaces and are more complex. Our focus here is to use relatively simple models to illustrate the convex duality between the price of a contingent claim and the process of cash borrowed in delta hedging. This reveals the root of the convexity in contingent claims. Interestingly, when hedging with a contingent claim instead of the underlying, a similar duality in the sense of generalized Fenchel conjugate holds. Correspondingly, this generalized duality leads to the generalized convexity of the contingent claims with many interesting applications. Much of the material presented in this chapter appear here for the first time.

Original languageEnglish (US)
Title of host publicationSpringerBriefs in Mathematics
PublisherSpringer Science and Business Media B.V.
Number of pages34
StatePublished - 2018

Publication series

NameSpringerBriefs in Mathematics
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201

ASJC Scopus subject areas

  • General Mathematics


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