The Annals of Applied Probability

Reduced-form framework under model uncertainty

Francesca Biagini and Yinglin Zhang

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1563869048

Digital Object Identifier
doi:10.1214/18-AAP1458

Mathematical Reviews number (MathSciNet)
MR3983342

Zentralblatt MATH identifier
07120714

Subjects
Primary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 60H30: Applications of stochastic analysis (to PDE, etc.) 91B30: Risk theory, insurance

Keywords
Sublinear expectation nondominated model reduced-form framework superhedging payment stream

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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