Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80882120120822Three Critical Models in Mathematical FinanceThree Critical Models in Mathematical Finance779610029FAAbdolsadeh NeisyDepartment of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, IranRoya Chamani AnbajiDepartment of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, IranLeili Shojaee ManeshDepartment of Mathematics, Computer and Statistics, AllamehTabataba'i University, Tehran, IranJournal Article20130611In this paper, using mathematical techniques, we are going to model some of the important financial markets. Due to the close relations between stock exchange and derivatives markets, we introduce models which also indicate the collaboration between mathematicians, statisticians, computer and finance researchers. Moreover, in this way, the weakness of the old models has been compensated, thus the new and modern models have been generated to improve financial and mathematical relations for new researches. The aim of this article is not to present the solution of new models, but it is to introduce one of the applied mathematics branchs in finance science. Finally, we make a model with three important problems in financial instruments, which transfer he partial-integral differential equations. Depending on market, application of inverse problems and free boundary value problems in finance science is being explained.In this paper, using mathematical techniques, we are going to model some of the important financial markets. Due to the close relations between stock exchange and derivatives markets, we introduce models which also indicate the collaboration between mathematicians, statisticians, computer and finance researchers. Moreover, in this way, the weakness of the old models has been compensated, thus the new and modern models have been generated to improve financial and mathematical relations for new researches. The aim of this article is not to present the solution of new models, but it is to introduce one of the applied mathematics branchs in finance science. Finally, we make a model with three important problems in financial instruments, which transfer he partial-integral differential equations. Depending on market, application of inverse problems and free boundary value problems in finance science is being explained.https://jamm.scu.ac.ir/article_10029_f0dc8061962edec402c3cfe99aff0b1b.pdf