Invariance times transfer properties  

作　　者：Stéphane Crepey 

机构地区：[1]Laboratoire de Probabilites,Statistique et Modelisation(LPSM),Sorbonne Universitéet Universite Paris Cite,CNRS UMR 800l,Paris,France

出　　处：《Probability, Uncertainty and Quantitative Risk》2024年第4期431-452,共22页概率、不确定性与定量风险(英文)

摘　　要：Invariance times are stopping times T such that local martingales with respect to some reduced filtration and an equivalently changed probability measure,stopped before T,are local martingales with respect to the original model filtration and probability mcasure.They arise naturally for modeling the default time of a dealer bank,in the mathematical finance context of counterparty credit risk.Assuming an invariance time endowed with an intensity and a positive Azéma supermartingale,this work establishes a dictionary relating the semimartingale calculi in the original and reduced stochastic bases,regarding conditional expectations,martingales,stochastic integrals,random mcasure stochastic integrals,martingale rcprcscntation propertics,scmimartingalc characteristics,Markov properties,transition semigroups and infinitesimal generators,and solutions of backward stochastic differential equations.

关 键 词：Progressive enlargement of filtration Invariance time Semimartingale calculus Markov process Backward stochastic differential equation Counterparty risk Credit risk 

分 类 号：O17[理学—数学]