A New Characterization of Random Times for Specifying Information Delay

Journal of Mathematical Sciences

Miura, Ryozo¹  Adachi, Takanori¹  Nakagawa, Hidetoshi¹ 

关键词: Credit risk;    default risk;    structural model;    stopping time;    random time;    information delay.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Weintroduceastochasticprocesscalledafollowerprocessconsistingofanon-decreasingsequenceofrandomtimes$f_t$whosevaluesdonotexceed$t$.Itwasoriginallyintroducedforrepresentinginformationdelayinstructuralcreditriskmodels.ThefollowerprocessisanextensionofatimechangeprocessintroducedbyGuo,JarrowandZenginthesensethateachcomponentofthefollowerprocessisnotrequiredtobeastoppingtime.Weintroduceaclassoffollowerprocessescalledidempotent,whichcontainsnaturalexamplesincludingfollowerprocessesdrivenbyrenewalprocesses.Weshowthatanyidempotentfollowerprocessishardtobeanexampleoftimechangeprocesses.Wedefineafiltrationmodulatedbythefollowerprocessandshowthatitisanaturalextensionofthecontinuouslydelayedfiltrationthatisthefiltrationmodulatedbythetimechangeprocess.WeshowthatconditionalexpectationsgivenidempotentfollowerfiltrationshavesomeMarkovpropertyinabinomialsetting,whichisusefulforpricingdefaultablefinancialinstruments.

【 授权许可】

Unknown