Random times with given survival probability and their \(\mathbb F\)-martingale decomposition formula
type: Item
instance of: scholarly article
title: Random times with given survival probability and their \(\mathbb F\)-martingale decomposition formula
zbMATH Open document ID: 1230.60047
author: Shiqi Song
author: Monique Jeanblanc
published in: Stochastic Processes and their Applications
publication date: 2011-06-15T00:00:00Z
review text: This research is motivated by credit risk modeling. The aim of the paper is to construct models with survival probability that have the form of a multiplicative decomposition of Azema's supermartingale. It is stated that this problem has several solutions and that an increasing family of martingales, combined with a stochastic differential equation, constitutes a natural way to construct these solutions. The enlargement of filtrations is considered that preserves the semimartingale property, and an explicit semimartingale decomposition formula for the solution is given. It is proved that any solution of this problem possessing the same semimartingale decomposition formula must satisfy the same stochastic differential equation.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 91G40
zbMATH DE Number: 5908040
zbMATH Keywords: progressive enlargement of filtration
zbMATH Keywords: semimartingale decomposition
zbMATH Keywords: multiplicative decomposition
zbMATH Keywords: credit risk
MaRDI profile type: Publication
full work available at URL: j.spa.2011.03.003
OpenAlex ID: W1967140988
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DOI: 10.1016/J.SPA.2011.03.003
description: scientific article; zbMATH DE number 5908040