The [phi]-Martingale

Frédéric Vrins and M. Jeanblanc
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M. Jeanblanc: Université d’Evry Val d’Essonne

No 2015022, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we focus on continuous martingales evolving in the unit interval [0,1]. We first review some results about the martingale property of solution to one-dimensional driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. One of these martingales proves to be analytically tractable, and received the specific name of [phi]-martingale. 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 coefficient (t, x) = g(t)h(x) that can be obtained via a time-homogeneous mapping of Gaussian processes. The approach is applied to the modeling of stochastic survival probabilities.

Keywords: continuous stochastic processes; Gaussian processes; bounded martingales; local martingales; Azema supermartingale; credit risk modeling (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2015-04-01
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (2)

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