Filtration Reduction and Completeness in Jump-Diffusion Models
Mathematical Finance
2025-11-07 v3 Probability
Pricing of Securities
Abstract
This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality.
Keywords
Cite
@article{arxiv.2304.06202,
title = {Filtration Reduction and Completeness in Jump-Diffusion Models},
author = {Karen Grigorian and Robert Jarrow},
journal= {arXiv preprint arXiv:2304.06202},
year = {2025}
}