幾類風(fēng)險(xiǎn)模型的破產(chǎn)理論及分紅問題的研究
發(fā)布時(shí)間:2020-12-06 14:52
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Gerber-Shiu函數(shù))和最優(yōu)分紅三個(gè)方面來研究了保險(xiǎn)中的若干問題。我們研究的風(fēng)險(xiǎn)模型大致分為兩類,一類是具有利率的風(fēng)險(xiǎn)模型,另一類是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)問題的研究我們一般是借助于對(duì)Gerber-Shiu函數(shù)的研究來展開的。而對(duì)于Gerber-Shiu函數(shù)的研究,則是通過隨機(jī)過程及隨機(jī)微分方程的知識(shí)得到它滿足的積分-微分方程及邊值問題,然后得到了它在指數(shù)索賠下的明確表達(dá)式以及Erlang(2)索賠下滿足的微分方程,并通過數(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)分紅問題的研究是通過研究折現(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)方面展開的。通過概率的手段推導(dǎo)出折現(xiàn)分紅總量均值的矩母函數(shù),高階矩滿足的積分-微分方程及邊值條件,或者通過粘性解理論來刻化最優(yōu)值函數(shù)。進(jìn)一步我們通過數(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:我們通過研究L(?)vy風(fēng)險(xiǎn)盈余過程的L(?)vy測(cè)度對(duì)應(yīng)的密度函數(shù)π的log-凸性...
【文章來源】:曲阜師范大學(xué)山東省
【文章頁數(shù)】:134 頁
【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 Du,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 Du,b
§3.3 Moments of Du,b
§3.4 Explicit expressions of Mu, y; b and Vn(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 Du,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
【文章來源】:曲阜師范大學(xué)山東省
【文章頁數(shù)】:134 頁
【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
§2.5 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
§3.5 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
+
§5.1 Introduction
1
u,b
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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