## The Annals of Applied Probability

### Reduced-form framework under model uncertainty

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 29, Number 4 (2019), 2481-2522.

Dates
Revised: September 2018
First available in Project Euclid: 23 July 2019

https://projecteuclid.org/euclid.aoap/1563869048

Digital Object Identifier
doi:10.1214/18-AAP1458

Mathematical Reviews number (MathSciNet)
MR3983342

Zentralblatt MATH identifier
07120714

#### Citation

Biagini, Francesca; Zhang, Yinglin. Reduced-form framework under model uncertainty. Ann. Appl. Probab. 29 (2019), no. 4, 2481--2522. doi:10.1214/18-AAP1458. https://projecteuclid.org/euclid.aoap/1563869048

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