Reduced-form framework under model uncertainty

TL;DR

This paper develops a framework for modeling credit and insurance markets under model uncertainty using sublinear expectations, extending classical reduced-form models to account for multiple, possibly mutually singular, probability measures.

Contribution

It introduces a sublinear conditional expectation for nondominated measures and establishes dynamic superhedging duality in continuous time under model uncertainty.

Findings

Extended reduced-form models to include multiple priors.

Established duality results for superhedging under uncertainty.

Bridged gap between robust financial and insurance market models.

Abstract

In this paper we introduce a sublinear conditional expectation with respect to a family of possibly nondominated probability measures on a progressively enlarged filtration. In this way, we extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other. Furthermore, we study the superhedging approach in continuous time for payment streams under model uncertainty, and establish several equivalent versions of dynamic robust superhedging duality. These results close the gap between robust framework for financial market, which is recently studied in an intensive way, and the one for credit and insurance markets, which is limited in the present literature only to some very specific cases.