几类风险模型的破产理论及分红问题的研究

发布时间：2020-12-06 14:52

　　本文分别从绝对破产,Gerber-Shiu期望折扣罚金函数（简称Gerber-Shiu函数）和最优分红三个方面来研究了保险中的若干问题。我们研究的风险模型大致分为两类,一类是具有利率的风险模型,另一类是L（?）vy风险模型。一、具有利率的风险模型:对于绝对破产问题的研究我们一般是借助于对Gerber-Shiu函数的研究来展开的。而对于Gerber-Shiu函数的研究,则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题,然后得到了它在指数索赔下的明确表达式以及Erlang（2）索赔下满足的微分方程,并通过数值分析得到贷款利息及存款利息对它的影响。对于最优分红问题的研究是通过研究折现分红总量均值的矩母函数/高阶矩,最优分红策略以及最优分红界几个方面展开的。通过概率的手段推导出折现分红总量均值的矩母函数,高阶矩满足的积分-微分方程及边值条件,或者通过粘性解理论来刻化最优值函数。进一步我们通过数据分析得到存款利息及贷款利息对折现分红总量均值函数及最优分红界的影响。二,L（?）vy风险模型:我们通过研究L（?）vy风险盈余过程的L（?）vy测度对应的密度函数π的log-凸性... 

【文章来源】：曲阜师范大学山东省

【文章页数】：134 页

【学位级别】：博士

【文章目录】：
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



本文编号：2901559

boshi