Representation of Martingales with Jumps and Applications to Mathematical Finance

Hiroshi Kunita

41 citations0/0 files storedAdvanced studies in pure mathematics

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

We study representations of martingales with jumps based on the filtration generated by a Lévy process. Two types of representation theorem are obtained. The first formula is valid for any martingale and written as the sum of the stochastic integral based on the Brownian motion and that based on the compensated Poisson random measure. See (0.1). The second formula is valid only for a process which is a martingale for any equivalent martingale measure. See (0.2). The latter representation formula is then applied to a problem in mathematical finance. The upper hedging strategy and the lower hedging strategy of a contingent claim is obtained through the representation kernel.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 41 citations exist upstream.

References

1998Methods of Mathematical Finance 1967On Square Integrable Martingales 1996Lectures on the Mathematics of Finance 2002Hedging of Contingent Claims under Transaction Costs

Cited by

2009RISK INDIFFERENCE PRICING IN JUMP DIFFUSION MARKETS 2010Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.