重尾分布下随机经济环境的破产概率渐近估计

发布时间：2018-07-10 18:10

本文选题：破产概率 + 随机利率　；参考：《南京农业大学》2014年硕士论文

【摘要】：本文的主要结果分为两个部分：首先在带投资收益的连续时间风险模型基础上考虑风险阀值,借助于伊藤随机过程相关理论和风险中性假设建立了双投资策略风险模型,并得到索赔过程属于D族且成对拟渐近独立时有限时间破产概率以及最终破产概率的渐近估计,且对其进行相应的数值模拟；其次讨论了基于多保单单一策略风险模型以及多保单双投资策略风险模型的破产概率渐近估计问题,得到其有限时间破产概率及最终破产概率的渐近估计结果,并对其进行了相应的数值模拟。本文结构安排如下：第一章简单叙述了破产论的发展历程,总结了破产论中研究风险模型的基本方向；同时对保险业的发展现状做了简单介绍,说明优化投资策略,提高投资回报率的现实依据。第二章为预备知识,首先介绍了几类常用的重尾分布族以及它们之间的隶属关系,以及马图谢夫斯卡指数、成对拟渐近独立和部分渐近关系的定义；并给出了伊藤随机过程的定义,以及伊藤公式等。第三章假设保险公司在不同盈余水平下采取不同的投资策略,从优化投资策略的角度出发,讨论了在双投资策略下保险公司破产概率的渐近估计问题。第四章讨论了多保单带投资收益的破产概率渐近估计问题,通过建立相互独立的多保单风险模型,最终得到有限时间破产概率和最终破产概率的渐近估计结果。
[Abstract]:The main results of this paper are divided into two parts: firstly, the risk threshold is considered on the basis of the continuous time risk model with investment return, and the risk model of double investment strategy is established with the help of Ito stochastic process correlation theory and risk neutral hypothesis. The asymptotic estimates of the finite time ruin probability and the final ruin probability are obtained when the claim process belongs to the D family and is pairwise asymptotically independent, and the corresponding numerical simulation is carried out. Secondly, the asymptotic estimation problem of ruin probability based on multi-policy single-policy risk model and multi-policy double-investment strategy risk model is discussed, and the asymptotic estimation results of its finite time ruin probability and final ruin probability are obtained. The corresponding numerical simulation is carried out. The structure of this paper is as follows: the first chapter briefly describes the development of bankruptcy theory, summarizes the basic direction of risk model research in bankruptcy theory, and introduces the current situation of insurance industry, explains the optimization of investment strategy. The realistic basis for improving the rate of return on investment. In the second chapter, we introduce several kinds of heavy-tailed distribution families and their subordinate relations, Matushevska exponent, and define the quasi-asymptotically independent and partial asymptotic relations. The definition of Ito stochastic process and the Ito formula are given. The third chapter assumes that insurance companies adopt different investment strategies under different earnings levels. From the point of view of optimizing investment strategies, the asymptotic estimation of the ruin probability of insurance companies is discussed in the case of double investment strategies. In chapter 4, we discuss the asymptotic estimation of ruin probability of multiple policies with investment income. By establishing independent multi-policy risk model, we obtain the asymptotic estimation results of ruin probability and final ruin probability in finite time.
【学位授予单位】：南京农业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F842.3;O212.1

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