We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additio...We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additional information related to a future value of the system.Since this puts the associated controlled systems outside the context of semimartingales,we apply anticipative white noise analysis,including forward integration and Hida-Malliavin calculus to study the problem.Combining this with Donsker delta functionals,we transform the insider control problem into a classical(but parametrised)adapted control system,albeit with a non-classical performance functional.We establish a sufficient and a necessary maximum principle for such systems.Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by Itô-Lévy processes.Finally,in the Appendix,we give a brief survey of the concepts and results we need from the theory of white noise,forward integrals and Hida-Malliavin calculus.展开更多
Erratum to:Commun.Math.Stat.(2015)3:365-421 DOI 10.1007/s40304-015-0065-y Unfortunately,in the original publication of the article some equations appeared incorrectly.The corrected equations are given below:•In(1.1)it...Erratum to:Commun.Math.Stat.(2015)3:365-421 DOI 10.1007/s40304-015-0065-y Unfortunately,in the original publication of the article some equations appeared incorrectly.The corrected equations are given below:•In(1.1)it should be added that the filtration H is assumed to be right-continuous,i.e.,that.展开更多
文摘We study optimal insider control problems,i.e.,optimal control problems of stochastic systemswhere the controller at any time t,in addition to knowledge about the history of the system up to this time,also has additional information related to a future value of the system.Since this puts the associated controlled systems outside the context of semimartingales,we apply anticipative white noise analysis,including forward integration and Hida-Malliavin calculus to study the problem.Combining this with Donsker delta functionals,we transform the insider control problem into a classical(but parametrised)adapted control system,albeit with a non-classical performance functional.We establish a sufficient and a necessary maximum principle for such systems.Then we apply the results to obtain explicit solutions for some optimal insider portfolio problems in financial markets described by Itô-Lévy processes.Finally,in the Appendix,we give a brief survey of the concepts and results we need from the theory of white noise,forward integrals and Hida-Malliavin calculus.
文摘Erratum to:Commun.Math.Stat.(2015)3:365-421 DOI 10.1007/s40304-015-0065-y Unfortunately,in the original publication of the article some equations appeared incorrectly.The corrected equations are given below:•In(1.1)it should be added that the filtration H is assumed to be right-continuous,i.e.,that.
