本文選題：破產(chǎn)概率 + 隨機(jī)利率�。� 參考：《南京農(nóng)業(yè)大學(xué)》2014年碩士論文

【摘要】：本文的主要結(jié)果分為兩個部分：首先在帶投資收益的連續(xù)時間風(fēng)險模型基礎(chǔ)上考慮風(fēng)險閥值,借助于伊藤隨機(jī)過程相關(guān)理論和風(fēng)險中性假設(shè)建立了雙投資策略風(fēng)險模型,并得到索賠過程屬于D族且成對擬漸近獨立時有限時間破產(chǎn)概率以及最終破產(chǎn)概率的漸近估計,且對其進(jìn)行相應(yīng)的數(shù)值模擬；其次討論了基于多保單單一策略風(fēng)險模型以及多保單雙投資策略風(fēng)險模型的破產(chǎn)概率漸近估計問題,得到其有限時間破產(chǎn)概率及最終破產(chǎn)概率的漸近估計結(jié)果,并對其進(jìn)行了相應(yīng)的數(shù)值模擬。本文結(jié)構(gòu)安排如下：第一章簡單敘述了破產(chǎn)論的發(fā)展歷程,總結(jié)了破產(chǎn)論中研究風(fēng)險模型的基本方向；同時對保險業(yè)的發(fā)展現(xiàn)狀做了簡單介紹,說明優(yōu)化投資策略,提高投資回報率的現(xiàn)實依據(jù)。第二章為預(yù)備知識,首先介紹了幾類常用的重尾分布族以及它們之間的隸屬關(guān)系,以及馬圖謝夫斯卡指數(shù)、成對擬漸近獨立和部分漸近關(guān)系的定義；并給出了伊藤隨機(jī)過程的定義,以及伊藤公式等。第三章假設(shè)保險公司在不同盈余水平下采取不同的投資策略,從優(yōu)化投資策略的角度出發(fā),討論了在雙投資策略下保險公司破產(chǎn)概率的漸近估計問題。第四章討論了多保單帶投資收益的破產(chǎn)概率漸近估計問題,通過建立相互獨立的多保單風(fēng)險模型,最終得到有限時間破產(chǎn)概率和最終破產(chǎn)概率的漸近估計結(jié)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.
【學(xué)位授予單位】：南京農(nóng)業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F842.3;O212.1

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本文編號：2114238