Locally Phi-Integrable Sigma-Martingale Densities for General Semimartingales

Tahir Choulli and Martin Schweizer
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Tahir Choulli: University of Alberta
Martin Schweizer: ETH Zurich and Swiss Finance Institute

No 15-15, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: A P-sigma-martingale density for a given stochastic process S is a local P-martingale Z>0 starting at 1 such that the product ZS is a P-sigma-martingale. Existence of a P-sigma-martingale density is equivalent to a classic absence-of-arbitrage property of S, and it is invariant if we replace the reference measure P with a locally equivalent measure Q. Now suppose that there exists a P-sigma-martingale density for S. Can we find another P-sigma-martingale density for S having some extra local integrability I_loc(P) under P? We show that the answer is always positive for one part of S that we identify, and we show that the complete answer depends in a precise quantitative way on the local integrability of the drift-to-jump ratio of the remaining "jumpy" part of S. Our proofs provide in addition new ideas and results in infinite-dimensional spaces.

Keywords: Sigma-martingale; equivalent martingale measures; Jacod decomposition; mathematical finance (search for similar items in EconPapers)
JEL-codes: C60 G10 (search for similar items in EconPapers)
Pages: 84 pages
Date: 2015-05
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1515

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