本文選題：廣義納什均衡問題　切入點：懲罰函數(shù)方法　出處：《大連理工大學(xué)》2013年博士論文　論文類型：學(xué)位論文

【摘要】：廣義納什均衡問題(GNEP)是納什均衡問題(NEP)的推廣,它允許每個參與人的目標(biāo)函數(shù)和策略集都可以依賴于競爭者的策略.故GNEP更適合于描述實際的競爭市場,但是數(shù)值算法還很少.此外,關(guān)于一般錐約束形式的GNEP還鮮有討論.本文研究了兩個求解GNEP的懲罰函數(shù)方法,以及一個半定錐約束的納什均衡問題；另外我們還討論了模糊環(huán)境的貨幣期權(quán)定價問題.隨著外匯市場交易量的迅速增長,貨幣期權(quán)的交易量也在逐漸增加.眾所周知,貨幣期權(quán)能夠有效地管理外匯市場的風(fēng)險.一般來說,數(shù)據(jù)是不能被完全精確記錄和搜集的,因此我們假設(shè)市場中的數(shù)據(jù)為模糊數(shù),考慮模糊環(huán)境的貨幣期權(quán)定價是合理的.具體來說,我們得到如下結(jié)果： 1.第三章中在討論了廣義納什均衡問題與擬變分不等式之間的等價關(guān)系之后,我們利用指數(shù)型和光滑化的y范數(shù)懲罰函數(shù)提出了兩個新的求解一般形式的廣義納什均衡問題的序列懲罰方法,其中序列中的每個懲罰問題都是C2光滑的懲罰納什均衡問題.我們證明了若光滑的懲罰納什均衡問題序列的解序列的聚點處EMFCQ成立,則此聚點是廣義納什均衡問題的一個解.進一步,我們把懲罰納什均衡問題的Karush-Kuhn-Tucher條件轉(zhuǎn)化為一個非光滑方程系統(tǒng),然后再用帶有Armijo線搜索的半光滑牛頓法來求解此系統(tǒng).最后,數(shù)值結(jié)果表明我們的兩個懲罰函數(shù)方法是有效的. 2.第四章中研究了求解半定錐約束的納什均衡問題的非精確牛頓法.首先,利用矩陣值的自然殘差函數(shù)將半定錐約束的納什均衡問題的Karush-Kunh-Tucker系統(tǒng)轉(zhuǎn)化為非光滑方程組.然后,證明了在一定條件下此方程組在解點處的Clarke廣義Jacobian是非奇異的.最后,應(yīng)用非精確牛頓法求解此方程組. 3.第五章中研究了模糊環(huán)境的貨幣期權(quán)定價問題.首先利用新的模糊集的0-水平集和支撐集的定義,我們修改了模糊數(shù)的定義,從而得到了一個關(guān)于模糊集的模糊值函數(shù)的基本命題.接著,我們利用擴展原理和上述基本命題,給出了一個用于歐式貨幣期權(quán)定價的Garman-Kohlhagen公式的模糊版本,并證明它是一個模糊數(shù).最后,通過辨識最優(yōu)權(quán)參數(shù),我們提出了一個利用權(quán)參數(shù)辨識的解模糊化方法.
[Abstract]:The generalized Nash equilibrium problem (GNEP) is the Nash equilibrium problem (NEP) of the promotion, the objective function and the strategy allows each participant can set depends on the competitor's strategy. Therefore, GNEP is more suitable to describe the actual market competition, but also a few numerical algorithm. In addition, the general form of the GNEP cone constraints little discussion. This paper studies the penalty function method and two for GNEP, and 1.5 fixed cone constrained Nash equilibrium problem; we also discussed the issue of currency option pricing fuzzy environment. With the rapid growth of foreign exchange market trading volume, trading volume of currency options are increasing gradually. As everyone knows, the currency option risk effectively the management of the foreign exchange market. Generally speaking, the data can not be completely accurate records and collected, so we assume that the market data as a fuzzy number, considering the fuzzy environment of monetary period The price of the right is reasonable. In particular, we get the following results:
1. in the third chapter, after the discussion of the equivalence between the generalized Nash equilibrium problem and variational inequality between, we use exponential smoothing norm and Y penalty function proposed sequence of generalized Nash equilibrium problem two new solving the general form of punishment, the punishment of each sequence are punished the Nash equilibrium of smooth C2. It is proved that if the point of EMFCQ solution sequence punish Nash equilibrium problem of smooth establishment, this point is a solution of the generalized Nash equilibrium problem. Further, we converted the Karush-Kuhn-Tucher condition to punish Nash equilibrium problem as a system of nonsmooth equations, and then with Armijo line search semi smooth Newton method is used to solve this system. Finally, the numerical results show that the two penalty function of our method is effective.
Inexact Newton method for the Nash equilibrium of 2. in the fourth chapter of solving semidefinite cone constraints. Firstly, the Karush-Kunh-Tucker system of the Nash equilibrium problem of natural residual function using matrix valued semidefinite cone constraints into nonsmooth equations. Then, it is proved that under certain conditions this equation is non singular in the Clarke generalized Jacobian solution point. Finally, the application of inexact Newton method for solving the equations.
3. the fifth chapter studies the problem of currency option pricing environment. Firstly, fuzzy definition of new fuzzy set 0- level sets and support sets, we modify the definition of fuzzy number, thus obtained the basic proposition of a fuzzy set of fuzzy valued function. Then, we use the extended principle and the basic proposition that gives a fuzzy version of a currency used for European option pricing formula of Garman-Kohlhagen, and it is proved that a fuzzy number. Finally, through the identification of optimal weight parameters, we propose a right to use the parameter identification of defuzzification method.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224

【參考文獻】

相關(guān)博士學(xué)位論文 前1條

1 袁艷紅;幾個廣義Nash均衡問題的求解方法[D];大連理工大學(xué);2012年

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本文編號：1598135