Conic Martingales from Stochastic Integrals

20 Pages Posted: 16 Mar 2018

See all articles by Monique Jeanblanc

Monique Jeanblanc

Université d'Évry - Departement de Mathematiques

Frédéric D. Vrins

Louvain Finance Center (LFIN), UC Louvain; Center for Operations Research and Econometrics (CORE), UC Louvain

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Date Written: April 2018

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 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.

Keywords: bounded martingale, diffusion process, stochastic differential equation, stochastic survival probability

Suggested Citation

Jeanblanc, Monique and Vrins, Frederic Daniel, Conic Martingales from Stochastic Integrals (April 2018). Mathematical Finance, Vol. 28, Issue 2, pp. 516-535, 2018. Available at SSRN: https://ssrn.com/abstract=3141582 or http://dx.doi.org/10.1111/mafi.12147

Monique Jeanblanc (Contact Author)

Université d'Évry - Departement de Mathematiques ( email )

rue du pere Jarlan
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Frederic Daniel Vrins

Louvain Finance Center (LFIN), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve, 1348
Belgium

HOME PAGE: http://www.uclouvain.be/frederic.vrins

Center for Operations Research and Econometrics (CORE), UC Louvain ( email )

Voie du Roman Pays 34
Louvain-la-Neuve,, B-1348
Belgium

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