Bi-revealed utilities in a defaultable universe: A new point of view on consumption  

作　　者：Nicole El Karoui Caroline Hillairet Mohamed Mrad 

机构地区：[1]LPSM,UMR CNRS 6632,Sorbonne Université,4 Place Jussieu,75005 Paris,France [2]CREST,UMR CNRS 9194,Ensae Paris,5 Avenue Henry Le Chatelier,91120 Palaiseau,France [3]LAGA,UMR CNRS 7539,UniversitéSorbonne Paris-Nord,99 Avenue Jean Baptiste Clement,93430 Villetaneuse,France

出　　处：《Probability, Uncertainty and Quantitative Risk》2024年第1期13-34,共22页概率、不确定性与定量风险（英文）

基　　金：This work is with the financial support of the“Chaire Risque Financier”of the“Fondation du Risque”,the Labex MME-DII.The authors's research is part of the ANR project DREAMeS(ANR-21-CE46-0002).

摘　　要：This paper investigates the inverse problem of bi-revealed utilities in a defaultable universe,defined as a standard universe(represented by a filtration F)perturbed by an exogenous defaultable time τ.We assume that the standard universe does not take into account the possibility of the default,thus τ adds an additional source of risk.The defaultable universe is represented by the filtration G up to time τ(τ included),where G stands for the progressive enlargement of F by T.The basic assumption in force is that τ avoids F-stopping times.The bi-revealed problem consists in recovering a consistent dynamic utility from the observable characteristic of an agent.The general results on bi-revealed utilities,first given in a general and abstract framework,are translated in the defaultable G-universe and then are interpreted in the F-universe.The decomposition of G-adapted processes X^(G) provides an interpretation of a Gcharacteristic X^(G)_(τ) stopped at τ as a reserve process.Thanks to the characterization of G-martingales stopped at τ in terms of F-martingales,we establish a correspondence between G-bi-revealed utilities from characteristic and F-bi-revealed pair of utilities from characteristic and reserves.In a financial framework,characteristic can be interpreted as wealth and reserves as consumption.This result sheds a new light on the consumption in utility criterion:the consumption process can be interpreted as a certain quantity of wealth,or reserves,that are accumulated for the financing of losses at the default time.

关 键 词：Bi-revealed utilities Defaultable euniverse Enlargement offiltration Preference criteria of wealth and consumption 

分 类 号：O17[理学—数学]