分紅策略下二元對偶風險模型的研究
發(fā)布時間：2018-11-05 19:34
【摘要】：最近幾年,隨著經(jīng)濟全球化的加劇,來自各個方面的風險越來越趨向復(fù)雜和多元化,為此人們越來越關(guān)注風險,于是學(xué)者們對風險理論特別是破產(chǎn)理論的研究也越來越深層次化。但大多數(shù)都是致力于研究保險公司的破產(chǎn)概率、破產(chǎn)時刻、破產(chǎn)前的瞬時盈余等問題,而結(jié)合紅利策略對紅利問題的研究還有待進一步深入。于是本文研究二元對偶風險模型,在分紅策略下對直到破產(chǎn)時刻為止紅利貼現(xiàn)值的期望的問題,同時考慮紅利發(fā)放會更加吸引投資者進行投資。所以對二元對偶風險模型下直到破產(chǎn)時刻為止紅利貼現(xiàn)值期望的研究具有一定的理論價值和現(xiàn)實指導(dǎo)意義,是一個非常有意義的課題。本文首先介紹了風險理論的一些基本知識和方法；然后考慮到現(xiàn)實中,保險公司會承擔不同的保險業(yè)務(wù)而遇到不同的風險,將一元對偶風險模型推廣到獨立二元,并加入閾值策略,對破產(chǎn)時刻為止紅利貼現(xiàn)值的期望進行了研究,得出它所滿足的積分微分方程,同時得出其對應(yīng)的解析表達式。從理論上并通過數(shù)值分析得出在二元的情況下,障礙策略依然是閾值的極限形式。最后又考慮到現(xiàn)實社會中往往不同的風險之間具有一定的關(guān)聯(lián)性,簡單的獨立二元模型已經(jīng)不切實際,而且現(xiàn)實中很多外界因素都會對收入產(chǎn)生影響。因此,又在閾值策略下研究了一種收入具有相依關(guān)系并由布朗運動驅(qū)動的二元對偶風險模型的紅利問題,最終得到了這種對偶風險模型下直到破產(chǎn)為止紅利貼現(xiàn)值期望的解析表達式。最后,對本文的研究結(jié)果作了一個總結(jié),給出了本文的展望。
[Abstract]:In recent years, with the intensification of economic globalization, the risks from various aspects have become more and more complex and diversified, so people are paying more and more attention to the risks. As a result, the study of risk theory, especially bankruptcy theory, is becoming more and more profound. However, most of them are devoted to the study of the bankruptcy probability, the time of bankruptcy, the instantaneous surplus before bankruptcy and so on. However, the study of dividend problem in combination with dividend strategy still needs to be further studied. In this paper, we study the dual risk model, and consider the expectation of the discount value of dividend until the time of bankruptcy under the dividend strategy, and consider that the dividend will attract investors to invest more. Therefore, the research on the expectation of dividend discounted value under the dualistic dual risk model until the time of bankruptcy has certain theoretical value and practical guiding significance, which is a very meaningful topic. This paper first introduces some basic knowledge and methods of risk theory. Then considering the reality, the insurance company will take on different insurance business and encounter different risks. The one-variable dual risk model will be extended to independent duality, and the threshold strategy will be added. In this paper, the expectation of the discount value of the dividend at the ruin time is studied, and the integral differential equation which it satisfies is obtained, and the corresponding analytical expression is obtained. Theoretically and numerically, it is concluded that the barrier strategy is still the limit form of threshold in the case of duality. Finally, considering that there is a certain correlation between different risks in real society, a simple independent binary model is impractical, and a lot of external factors will have an impact on income in reality. Therefore, the dividend problem of a dual risk model with income dependence and driven by Brownian motion is also studied under threshold strategy. Finally, the analytical expression of the expectation of dividend discounted value under the dual risk model is obtained. Finally, the research results of this paper are summarized and the prospect of this paper is given.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O211.67
本文編號：2313156
[Abstract]:In recent years, with the intensification of economic globalization, the risks from various aspects have become more and more complex and diversified, so people are paying more and more attention to the risks. As a result, the study of risk theory, especially bankruptcy theory, is becoming more and more profound. However, most of them are devoted to the study of the bankruptcy probability, the time of bankruptcy, the instantaneous surplus before bankruptcy and so on. However, the study of dividend problem in combination with dividend strategy still needs to be further studied. In this paper, we study the dual risk model, and consider the expectation of the discount value of dividend until the time of bankruptcy under the dividend strategy, and consider that the dividend will attract investors to invest more. Therefore, the research on the expectation of dividend discounted value under the dualistic dual risk model until the time of bankruptcy has certain theoretical value and practical guiding significance, which is a very meaningful topic. This paper first introduces some basic knowledge and methods of risk theory. Then considering the reality, the insurance company will take on different insurance business and encounter different risks. The one-variable dual risk model will be extended to independent duality, and the threshold strategy will be added. In this paper, the expectation of the discount value of the dividend at the ruin time is studied, and the integral differential equation which it satisfies is obtained, and the corresponding analytical expression is obtained. Theoretically and numerically, it is concluded that the barrier strategy is still the limit form of threshold in the case of duality. Finally, considering that there is a certain correlation between different risks in real society, a simple independent binary model is impractical, and a lot of external factors will have an impact on income in reality. Therefore, the dividend problem of a dual risk model with income dependence and driven by Brownian motion is also studied under threshold strategy. Finally, the analytical expression of the expectation of dividend discounted value under the dual risk model is obtained. Finally, the research results of this paper are summarized and the prospect of this paper is given.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O211.67
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