hjb方程在最優(yōu)投資策略中的應用

1、學校代碼: 10270 分類號: O29 學號：122200706碩 士 學 位 論 文論 文 題 目 HJB方程在最優(yōu)投資策略中的應用學 院 數(shù)理學院專 業(yè) 應用數(shù)學研 究 方 向 金融數(shù)學研 究 生 姓 名 周 翠指 導 教 師 張 寄 洲 教 授完 成 日 期 二零一五年三月萬方數(shù)據(jù)AbstractIn the research domain of portfolio and risk management, some optim

2、al and control problemsare involved. Due to the randomness of the environment, these control problems are characterizedby stochastic optimal control model. Generally, in these control models, the price of equities,assets

3、 of firms and other market variables are taken as state variables. The portfolio ratio andstopping time of trade are considered as control variables. The objective of control is to maximizethe total return or minimize th

4、e risk of investment. The main method to solve the optimal controlproblem is the dynamic programming principle(DPP). And a Hamilton-Jacobi-Bellman(HJB) canbe derived by DPP. In this article, two kinds of control problems

5、 are studied. Under the back-ground of insurance company, in the case that the investment portfolio contains European calloptions, and the objective of control is to maximize the total return. The other one, under thebac

6、kground of network lending, assuming the firm of P2P invest to a bond of credit risk, and theobjective of control is to maximize the risk of investment. These two problems, the closed-formsolutions of the HJB Equation ar

7、e both solved, and the verification theorem is also proved. Final-ly, the influence of parameters on the solution are analyzed to illustrate the results. This article isdivided into five chapters.The first chapter illust

8、rates the research background and the research methods and status indomestic and overseas. In chapter two, we simply reviewed the dynamic programming principleand the multidimensional It? o formula, which are the main re

9、search methods and theoretical basisthroughout this article.In chapter three, optimal investment and proportional reinsurance strategy with options isstudied. In the perspective of insurance company, we consider the opti

10、mal investment and propor-tional reinsurance strategy in the case that the investment portfolio contains European call optionsunder the Black-Scholes model. By using stochastic control method, the utility maximizationmod

11、el and the corresponding HJB equation are obtained. What’s more, the closed-form solutionsof the HJB Equation is solved, and the verification theorem is also proved. Finally, the influenceof parameters on the solution is

12、 analyzed to illustrate the result.In chapter four, we measure the risk of P2P firm. In the view of P2P firm, we discuss theoptimal investment strategy in the case that P2P invest to risk equities and a bond of credit ri

13、sk.The objective is to minimize the risk on the condition that the terminal wealth is a constant. Tosolve this problem, the mean-variance model is used. The mean - variance problem can be seenas an optimal control proble