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 ...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.展开更多
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).
文摘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.
