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  1. Stochastic Differential Equations and Related Topics - Jin Ma
  2. mathematics and statistics online
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The study on credit risk models with partial information and optimal liquidation problems are aiming at exploring new modeling aspects in stochastic finance.

Three problems are directly related to issues in finance and insurance, using the tools developed in the proposed theoretical studies, while one theoretical problem arises from a real project with a local bank in LA. Several parts of the proposed research involve Ph. D students and postdoctoral fellows.

1.5 Solving Stochastic Differential Equations

D students involved in the proposed research are more likely to obtain internships from the local banks, and some might lead to permanent employment. The NSF Grant DMS resulted in a series of research papers in three areas of theoretical and applied probability: I stochastic differential equations; II stochastic partial differential equations; and III stochastic control and stochastic finance theory.


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The projects completed under the support of the grant, although different in nature, are often connected and mutually motivating. Several theoretical results in stochastic differential equations are initiated by and applied to respective problems in stochastic finance and insurance, and others are independent problems that are interesting in their own rights.

Stochastic Differential Equations and Related Topics - Jin Ma

During the past three years, the PI completed 13 papers under the support of the grant. Among them 6 papers have already appeared, 2 papers are in press, 2 papers are conditionally accepted, and 3 papers are under review.


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Click the Internet Zone. Forward-backward stochastic differential equations and their applications in finance Abstract: In this paper we present some results concerning the solvability of the adapted solutions to a class of forward-backward stochastic differential equations over an arbitrarily prescribed time duration, and several applications of such equations in mathematical finance. In particular, we introduce a direct scheme called "four step scheme" initiated by Ma-Protter-Yong , which enables one to derive the explicit relations between the forward and backward components of the adapted solutions.

Using the extensions of such a scheme in different directions, we then study some problems in finance including a console rate problem, a problem of hedging options for a large investor, and a stochastic Black-Scholes formula.


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