## Stability of Sigma-Martingale Densities in L log L Under an Equivalent Change of Measure

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Date

2011-01Type

- Working Paper

ETH Bibliography

yes
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Abstract

An equivalent sigma-martingale measure (E-sigma-MM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an E-sigma-MM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if we replace the reference measure P with an equivalent measure Q. Now suppose that there exists an E-sigma-MM for S such that the density dR/dP is in L log L(P). Does this property also remain invariant if we replace P by some equivalent Q? We prove that the answer is Yes if one imposes instead of a global only a local integrability requirement. Show more

Publication status

publishedJournal / series

NCCR FINRISK working paperVolume

Publisher

National Centre of Competence in Research Financial Valuation and Risk ManagementSubject

Sigma-martingale; Equivalent martingale measures; Jacod decomposition; Mathematical financeOrganisational unit

03658 - Schweizer, Martin / Schweizer, Martin
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ETH Bibliography

yes
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