带投资收益的更新风险模型的渐近分析及其应用研究

发布时间：2018-03-16 06:43

本文选题：综合风险模型　切入点：Lévy过程　出处：《浙江工商大学》2016年博士论文　论文类型：学位论文

【摘要】：极端事件,包括极端自然风险与极端金融风险,常常会导致严重的后果。在保险业中,许多重大的保险风险莫过于重大灾害事件而导致的巨额索赔,一次巨灾索赔可以导致保险公司偿付能力不足甚至破产：与之相对应的是金融风险,主要包括保险资金的投资风险与利率变动风险,一次投资失败造成的后果是灾难性的。如何应对和防范极端风险,是现代风险管理的关键问题之一。经典的风险模型对金融衍生品的投资因素往往不予考虑。但是,在现代社会中,一方面随着保险业的发展,保险公司资产规模不断扩大,拥有巨额资金投放到金融市场中,另一方面,金融衍生工具的不断创新使得投资渠道日益多样化,凭借雄厚的资金实力和专业的投资部门,保险公司成为了金融市场上举足轻重的机构投资者。因此在考虑传统的理赔风险之外,对于投资资本市场所带来的金融风险的度量和管理显得尤为迫切,它直接关系到保险公司的偿付能力。考虑带有金融风险的风险模型应运而生,并逐渐成为风险理论中的重要分支。破产概率是风险理论的核心概念,它是度量保险公司经营稳健性的一个重要指标。极端事件对应的概率分布往往是重尾的,重尾情形下的精细大偏差估计为与再保险有关的风险度量的测算提供了理论基础。本文主要在重尾综合风险模型的框架下,研究了破产概率的一致渐近估计,索赔额现值的精细大偏差问题,并对影响该模型盈余过程的各种因素进行模拟分析,运用所得理论结果,应用到风险测度以及最优投资策略等问题。具体内容如下：第一章首先阐述了本文的研究背景和研究意义,分别从模型,问题的角度论证选题的合理性和可行性；其次对有关风险模型的研究脉络和研究现状进行了梳理和总结；最后在此基础上提出了本文研究的主要内容。第二章给出了本文主要结果所需的预备知识,涵盖以下两个方面：首先是Lévy过程的相关理论,主要包括Lévy-Khinchine表示定理,Lévy-It(?)分解,Lévy过程的分类,Lévy过程的It(?)公式以及随机指数等内容；其次介绍了重尾分布族的定义和分类,特别是对有关次指数分布族,控制变换族和正则变换族的性质做了系统总结。第三章主要研究了具有时依结构的重尾综合风险模型中有限时破产概率的一致渐近估计。首先引入了综合风险模型,该模型假定保险公司将资产盈余按一定比例投资到无风险的货币市场和有风险的资本市场,假定风险投资对数收益率过程为Lévy过程,并将之纳入到风险理论的框架。然后在该模型中考虑索赔额和索赔时间间隔满足特定的相依结构,并对具体的coupla函数验证了该假定的合理性。假定索赔额分布F∈LN D,在一定条件下,分别得到了在完全风险投资情形和固定混合投资情形下有限时破产概率的一致渐近估计,并从条件和结论的角度比较了两种情形下的结果,以及简要介绍了该结果在风险管理的应用,最后通过构建一系列引理对主要结果进行了证明。第四章从精细大偏差的角度对索赔额随机折现值展开研究。本章假定该模型中索赔额与对应的时间间隔相互独立,且索赔额分布F∈ R-α。,在保险风险为主要风险的条件下,分别得到了索赔额方差存在情形下和期望存在但方差不存在情形下索赔额随机折现值部分和的精细大偏差,然后将之推广到随机和的情形。在此基础上,我们指出该结论对于净索赔额的随机折现值和中心化情形也是成立的。由于α的不同取值范围,导致相应性质的差异,使得证明方法也因之不同,特别是期望存在但方差不存在情形下采取了双重截尾技巧并高度依赖于正则变换族的性质,我们通过构建一系列引理对主要结果进行了证明。第五章首先对综合风险模型的盈余过程进行模拟分析,对投资过程、索赔额分布以及投资策略不同的情景设置对盈余过程的影响程度做了定性分析；其次利用前几章得到的相关结论,从理论上探讨了综合风险模型框架下保险公司在一个给定时间段内的最优投资策略。本章考虑了两种约束条件,一种是终期盈余的方差,另一种是有限时破产概率,并对不同的情景设定进行数值分析,刻画其对最优投资策略的影响,结果表明,相对均值方差模型,有限时破产概率约束更适合于保险公司的风险管理。第六章简要总结全文的研究工作和主要创新点,并指出需要完善和有待进一步研究的问题。
[Abstract]:Extreme events, including extreme natural risk and extreme financial risks, often lead to serious consequences. In the insurance industry, huge claims caused many major insurance risk is a major disaster event, a catastrophe claims can lead to the insolvency of the insurance company or even bankruptcy: the corresponding financial risk is mainly. Including the insurance fund investment risk and interest rate risk, an investment failure caused by catastrophic consequences. How to deal with and prevent the risk of extreme, is one of the key problems in modern risk management. Not often consider the investment risk factors the classic model of financial derivatives. However, in modern society, on the one hand with the the development of the insurance industry, the insurance company asset size continues to expand, with huge amounts of money to the financial market, on the other hand, continuous innovation of financial derivatives make investment Information channels are becoming increasingly diversified, with strong financial strength and professional investment department, the insurance company has become an important institutional investor in financial market. Therefore, in consideration of traditional settlement risk, especially in measurement and management of investment in the capital market financial risks is particularly urgent, it is directly related to the solvency of insurance company. Consider the risk model with financial risk came into being, and gradually become an important branch of risk theory. Ruin probability is the core concept of risk theory, it is an important index to measure the sound management of insurance company. The corresponding probability distribution of extreme events is often heavy tailed, precise large deviation of heavy tailed case of estimating measure for risk and related reinsurance provides a theoretical basis. This paper mainly in the framework of heavy tailed comprehensive risk model, bankruptcy probability research Estimation of asymptotic rate, large deviations of claim value, and analyzed the effects of various factors on the model of the surplus process, using the theoretical results, applied to the risk measurement and the optimal investment strategy and other issues. The specific contents are as follows: the first chapter first introduces the research background and research significance, respectively. From the model, the rationality and feasibility of the perspective of the topic; secondly the research context and research status on the risk model is reviewed and summarized; finally put forward based on the main contents of this paper. The preliminary knowledge required for the second chapter gives the main results of this paper, covering the following two aspects: the first is the theory of L vy process, including L e vy-Khinchine L e vy-It representation theorem, (?) decomposition, classification of L vy process, L vy process It (?) formula and random index Content; secondly introduces the definition and classification of heavy tailed distribution group, especially for the exponential distribution, the nature of family control transform and canonical transformation family are systematically summarized. The third chapter is studied according to the comprehensive risk of heavy tailed model structure in finite time ruin probability estimation asymptotically. First, the introduction of a comprehensive risk model, the model assumes that the surplus assets according to a certain proportion of investment to the risk-free money market and capital market risk of insurance companies, investment risk assumed logarithmic return process for L vy process, and will be incorporated into the framework of risk theory. Then the model considered the claims and senior high school entrance examination meet the claim interval dependent structure specific, and the specific function of coupla to verify the rationality of the assumption. The assumption that the claim size F, LN D, under certain conditions, were obtained in total risk investment Uniformly asymptotic estimate of finite time ruin probability with the fixed and mixed investment situation, and from the condition and conclusion of comparison of two case results, and briefly introduces the results in the application of risk management, finally construct a series of Lemmas on the main results were proved. The fourth chapter from large deviations the angle of claim random discounted value is researched. This chapter assumes the model of claim with the corresponding time intervals are independent of each other, and the claim amount distribution of F and R- alpha., in the insurance risk is the main risk conditions, obtained claim amount variance existing circumstances and expectations exist but the variance does not exist under the condition of claim random discounted value of precise large deviations and, and then extended to random and situation. On this basis, we point out the conclusion for the stochastic discount net claims value and the center of the situation The shape is established. Because of the different range of alpha, lead to differences in the corresponding properties, so the proof method for different, especially the expected variance exists but does not exist under the condition of taking a double truncated skills and highly dependent on the nature of canonical transformation of family, we construct a series of lemmas to demonstrate the main results. The fifth chapter of the surplus process integrated risk model of the simulation analysis of the investment process, claim amount distribution and investment strategies of different situations influence on earnings in the process of doing qualitative analysis; followed by the previous chapter conclusions, discusses the optimal investment strategy in a given period of time the insurance company the comprehensive risk model in theory. This chapter considers the two constraint conditions, a final stage is the variance of earnings, the other is a finite time ruin probability, and the different Set the scene for numerical analysis, describe its impact on the optimal investment strategy. The results show that the relative mean variance model, the risk management of finite time ruin probability constraint is more suitable for the insurance company. The sixth chapter summarizes the whole thesis and main innovations, and pointed out the need to improve and further study of the problem.

【学位授予单位】：浙江工商大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F840.31;F830.59

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