| MULTI-DIMENSIONAL
GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL
FINANCE |
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| 作者姓名： | 胡耀忠 |
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| 作者单位： | Department of Mathematics，University of Kansas，405 Snow Hall，Lawrence，KS 66045-2142. USA Wuhan Institute of Physics and Mathematics，Chinese Academy of Sciences，Wuhan 430071，China |
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| 基金项目： | the General Research Fund of the University of Kansas. |
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| 摘 要： | 1 IntroductionThe solution of the following stochastic differential equationis called the geometric Brownian motion, where a(t), b(t) are deterministic functions of ti ac isa Brownian motion, and ddt is the It6 integral. This equation has been successfully applied tothe financial problems such as modeling the prices of stocks, sc.e for example, 81, 7], 14], 13],19], 21]. When the initial condition is given, i.e. xo = x, the solution isIt is known that in the financial market, it is als…
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MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE |
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| Hu Yaozhong.MULTI-DIMENSIONAL
GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL
FINANCE[J].Acta Mathematica Scientia,2000,20(3):341-358. |
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| Authors: | Hu Yaozhong |
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| Abstract: | The solutions of the following bilinearstochastic differential equation are stud-ied (X) where Atk, Bt are (deterministic)continuous matrix-valued functions of t and w1(t),..., wm(t) are m independent standard Brownian motions. Conditions are given such thatthe solution is positive if the initial condition is positive.The equation the most probable path must satisfy is also derived and applied to a mathematicalfinance problem. |
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| Keywords: | Multi-dimensional geometric Brownian motions Onsager-Machlup functions most probable path positivity most likely interest rate |
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