相對于經(jīng)典的金融保險模型而言,馬氏調(diào)節(jié)的金融保險模型似乎更能適應(yīng)現(xiàn)實中的金融保險數(shù)據(jù)。在風險理論中,馬氏調(diào)節(jié)的風險模型有這樣一個優(yōu)點:保險公司可以隨外界環(huán)境（天氣,經(jīng)濟,政府政策等）的改變而調(diào)節(jié)自身的保險政策。舉個例子來說吧,在汽車保險中,天氣環(huán)境的好壞是影響事故發(fā)生的重要因素。在不同的天氣環(huán)境下,汽車保險中索賠的分布以及索賠在一定時間內(nèi)發(fā)生的強度將會有很大的不同。因此,不同的天氣環(huán)境下,保險公司的保險政策也將會有很大的不同,比如說,保費的收取將會隨天氣環(huán)境的變化而變化。在金融理論中,著名的Black-Scholes-Merton金融市場是基于幾何布朗運動來描述標的資產(chǎn)（股票）的價格變化的。但是越來越多的實證研究表明,幾何布朗運動并不能描述一些標的資產(chǎn)價格數(shù)據(jù)中的重要實證結(jié)果,比如,標的資產(chǎn)價格分布的重尾性質(zhì),標的資產(chǎn)價格的方差應(yīng)該是隨時間變化而變化的等等。Hardy[75]對馬氏調(diào)節(jié)的金融市場模型與其他模型對現(xiàn)實金融數(shù)據(jù)的適合程度進行了比較并得出結(jié)論,馬氏調(diào)節(jié)的金融市場模型對現(xiàn)實金融數(shù)據(jù)的適合程度明顯優(yōu)于其他一些比較常用金融市場模型�；谝陨显�,馬氏調(diào)節(jié)模型在金融保險理論中正變得越... 

【文章來源】：南開大學(xué)天津市 211工程院校 985工程院校 教育部直屬院校

【文章頁數(shù)】：221 頁

【學(xué)位級別】：博士

【文章目錄】：
摘要
Abstract
1 Introduction
    1.1 Background
    1.2 Organization and Main Contents of This Dissertation
2 Preliminaries
    2.1 Representation of Double Martingales
    2.2 Markov Chain
    2.3 Markov-Modulated Lévy Processes
    2.4 It(o|
)'s Formula for Generalized Markov-Modulated SDEs
3 Ruin Problems in a Markov-Modulated Compound Poisson Model
    3.1 Introduction
    3.2 The Markov-Modulated Compound Poisson Model
    3.3 Gerber-Shiu Discounted Penalty Functions
        3.3.1 Integro-differential Equations of Gerber-Shiu Discounted Penalty Function
        3.3.2 The Value of φ(O)
    3.4 Explicit Expressions of Gerber-Shiu Discounted Penalty Functions
        3.4.1 Formulas for φ_1(O) and φ_2(O)
        3.4.2 Explicit Expressions of α_1(u) and φ_2(u) for K_n-family Claim Size Distributions
    3.5 Numerical Illustrations
4 Complete Markovian Regime-Switching Market via Double Martingales
    4.1 Introduction
    4.2 Markovian Regime-Switching Market
    4.3 Some Results for Markov-Modulated Brownian Motion
        4.3.1 Characterization of Markov-Modulated Brownian Motion
        4.3.2 A Measure Change for Markov-modulated Brownian Motion
    4.4 Complete the Markovian Regime-Switching Market and Hedging
    4.5 Equivalent Martingale Measures
5 Portfolio Selection in the Enlarged Markovian Regime-Switching Market
    5.1 Introduction
    5.2 Enlarged Markovian Regime-Switching Market
        5.2.1 Markovian Regime-Switching Market
        5.2.2 Enlarging the Markovian Regime-Switching Market
    5.3 Arbitrage-Free and Completeness of the Enlarged Market
    5.4 Optimization Problems
        5.4.1 Logarithmic Utility
        5.4.2 Power Utility
    5.5 Comparisons of Optimization Problems in Enlarged and Original Market
6 Portfolio Optimization in Extended Markovian Regime-Switching Market
    6.1 Introduction
    6.2 Problem Formulation
    6.3 No Shorting Constraint
        6.3.1 Logarithmic Utility
        6.3.2 Power Utility
    6.4 No Constraint
        6.4.1 Logarithmic Utility
        6.4.2 Power Utility
7 Reinsurance and Investment in Extended Regime-Switching Market
    7.1 Introduction
    7.2 Extended Markovian Regime-Switching Market and Insurance Model
    7.3 Maximize the Utility and HJB Equation
    7.4 Solution of HJB Equation for Exponential Utility Function
    7.5 The Verification Theorem
    7.6 Some Special Cases of Our Model
    7.7 Numerical Example
8 Mean-Variance Problem in the Markov-Switching Jump-Diffusion Market
    8.1 Introduction
    8.2 Markov-Switching Jump-Diffusion Market and Feasibility of M-V Problem
    8.3 Solution to Unconstrained Markov-Modulated Stochastic LQ Problem
    8.4 Efficient Portfolio and Efficient Frontier
9 Optimal Reinsurance and Investment in a Hidden Markov Model
    9.1 Introduction
    9.2 Insurance Risk Model and Hidden Markovian Regime Switching Market
    9.3 Separation Principle
    9.4 HJB-equation Approach
Bibliography
Index
Resume and Publications
Acknowledgements



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