本文分別從絕對(duì)破產(chǎn),Gerber-Shiu期望折扣罰金函數(shù)（簡(jiǎn)稱(chēng)Gerber-Shiu函數(shù)）和最優(yōu)分紅三個(gè)方面來(lái)研究了保險(xiǎn)中的若干問(wèn)題。我們研究的風(fēng)險(xiǎn)模型大致分為兩類(lèi),一類(lèi)是具有利率的風(fēng)險(xiǎn)模型,另一類(lèi)是L（?）vy風(fēng)險(xiǎn)模型。一、具有利率的風(fēng)險(xiǎn)模型:對(duì)于絕對(duì)破產(chǎn)問(wèn)題的研究我們一般是借助于對(duì)Gerber-Shiu函數(shù)的研究來(lái)展開(kāi)的。而對(duì)于Gerber-Shiu函數(shù)的研究,則是通過(guò)隨機(jī)過(guò)程及隨機(jī)微分方程的知識(shí)得到它滿(mǎn)足的積分-微分方程及邊值問(wèn)題,然后得到了它在指數(shù)索賠下的明確表達(dá)式以及Erlang（2）索賠下滿(mǎn)足的微分方程,并通過(guò)數(shù)值分析得到貸款利息及存款利息對(duì)它的影響。對(duì)于最優(yōu)分紅問(wèn)題的研究是通過(guò)研究折現(xiàn)分紅總量均值的矩母函數(shù)/高階矩,最優(yōu)分紅策略以及最優(yōu)分紅界幾個(gè)方面展開(kāi)的。通過(guò)概率的手段推導(dǎo)出折現(xiàn)分紅總量均值的矩母函數(shù),高階矩滿(mǎn)足的積分-微分方程及邊值條件,或者通過(guò)粘性解理論來(lái)刻化最優(yōu)值函數(shù)。進(jìn)一步我們通過(guò)數(shù)據(jù)分析得到存款利息及貸款利息對(duì)折現(xiàn)分紅總量均值函數(shù)及最優(yōu)分紅界的影響。二,L（?）vy風(fēng)險(xiǎn)模型:我們通過(guò)研究L（?）vy風(fēng)險(xiǎn)盈余過(guò)程的L（?）vy測(cè)度對(duì)應(yīng)的密度函數(shù)π的log-凸性... 

【文章來(lái)源】：曲阜師范大學(xué)山東省

【文章頁(yè)數(shù)】：134 頁(yè)

【學(xué)位級(jí)別】：博士

【文章目錄】：
中文摘要
ABSTRACT
Chapter 1 Preliminaries
    §1.1 Some basic risk models
    §1.2 About optimal dividend problems
    §1.3 Confluent hypergeometric equation
Chapter 2 Dividend payments in the classical risk model under absolute ruin
    §2.1 Introduction
u,b">    §2.2 Moment generating function of Du,b

    §2.3 Moments of D_u,b

    §2.4 Explicit expressions for exponential claims
    §2.5 Optimal dividend barrier for exponential claims
    §2.6 Numerical analysis for Erlang（2） claim sizes
    §2.7 The Gerber-Shiu expected discounted penalty function
Chapter 3 Optimal dividends in the classical risk model with credit and debit interests under absolute ruin
    §3.1 Introduction
u,b">    §3.2 Moment generating function of D_u,b

    §3.3 Moments of D_u,b

    §3.4 Explicit expressions of M_{u, y; b} and V_n（u, b）
    §3.5 Optimal choice of dividend barrier for exponential claims
    §3.6 The Laplace transform of absolute ruin time
Chapter 4 The perturbed compound Poisson risk process with in vestment and debit interest
    §4.1 Introduction
    §4.2 The stochastic Dirichlet problem
    §4.3 Integro-differential equations
    §4.4 Integral equations
+">    §4.5 A renewal equation and asymptotic results for Φ₊

    §4.6 Explicit results for exponential claims Φ₊

Chapter 5 On the perturbed compound Poisson risk model under absolute ruin with debit interest and a constant dividend barrier
    §5.1 Introduction
1（u, b）">    §5.2 Integro-differential equations for V₁（u, b）
u,b">    §5.3 Moment generating function and higher moments of D_u,b

    §5.4 The Gerber-Shiu expected discounted penalty function
Chapter 6 Optimal dividend strategy in the perturbed compound Poisson risk model with investment interest
    §6.1 Introduction
    §6.2 Hamilton-Jacobi-Bellman equation
    §6.3 Construction of the optimal strategy
    §6.4 Examples
Chapter 7 Optimality of the barrier strategy for spectrally negative Levy risk processes
    §7.1 Introduction
    §7.2 Preliminaries on log-convex functions and related functions
    §7.3 Convex solutions for integro-differential equations
    §7.4 The optimality of the barrier strategy
References
Acknowledgements



本文編號(hào)：2901559

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