Conic martingales from stochastic integrals

Monique Jeanblanc and Frédéric Vrins

Mathematical Finance, 2018, vol. 28, issue 2, 516-535

Abstract: In this paper, we introduce the concept of conic martingales. This class refers to stochastic processes that have the martingale property but that evolve within given (possibly time†dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. Specific attention is paid to martingales in [0, 1]. One of these martingales proves to be analytically tractable. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion, and geometric Brownian motion) having a separable diffusion coefficient σ(t,y)=g(t)h(y) and that can be obtained via a time†homogeneous mapping of Gaussian diffusions. The approach is exemplified by modeling stochastic conditional survival probabilities in the univariate and bivariate cases.

Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
https://doi.org/10.1111/mafi.12147

Related works:
Working Paper: Conic martingales from stochastic integrals (2018)
Working Paper: Conic Martingales from Stochastic Integrals (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:28:y:2018:i:2:p:516-535

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0960-1627

Access Statistics for this article

Mathematical Finance is currently edited by Jerome Detemple

More articles in Mathematical Finance from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().