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The Application of PDE in Stochastic Optimal Control

Author: LiXue
Tutor: YaoMiaoXin
School: Tianjin University
Course: Applied Mathematics
Keywords: Stochastic optimal control Utility function Value function HJB equation
CLC: F830
Type: Master's thesis
Year: 2007
Downloads: 197
Quote: 0
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Abstract


The relevant theory of stochastic optimal control a wide range of applications , financial investment is one of them . This paper describes the theory of optimal control problems based on the theory of partial differential equations under random , based on the use of the maximum principle to solve the stochastic optimal control problem , and the use of this method to study the pension insurance fund in the financial markets the problem of the optimal investment strategy . Risk-free and risky assets of pension funds to invest in the market can be a good random Wiener process description, additional inflation and wage income levels , can constitute a complete financial market , so that the model closer to the actual . Finally , by introducing the function of the value of the stochastic optimal control ( that is, and the investor 's utility function is directly related to ) its utility-maximizing investors' optimal investment ratio , ie, the optimal investment strategy . To make the model more complete study of the investment model can also be added transaction fees , bonuses and dividends for investors , it is even more actual operability . Investment strategies are based on the value of the function , but the general second-order partial differential equation is difficult to seek analytical expression . How to apply the numerical method to solve pending further study .

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory
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