Random times with given survival probability and their \(\mathbb F\)-martingale decomposition formula
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.
scientific article; zbMATH DE number 5908040
scientific article