Locally Ф-integrable σ-martingale densities for general semimartingales
METADATA ONLY
Loading...
Author / Producer
Date
2015-06-05
Publication Type
Working Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
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.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
15 (15)
Pages / Article No.
Publisher
University of Geneva
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
σ-martingale; Equivalent martingale measures; Jacod decomposition; Mathematical finance
Organisational unit
03658 - Schweizer, Martin / Schweizer, Martin