發(fā)布時(shí)間：2018-05-15 06:33

  本文選題：對(duì)偶風(fēng)險(xiǎn)模型 + Parisian延遲��； 參考：《曲阜師范大學(xué)》2017年碩士論文

【摘要】：在關(guān)于破產(chǎn)問(wèn)題的論文中,一般習(xí)慣作直接性的評(píng)價(jià).例如,關(guān)于破產(chǎn)時(shí)刻的確定,當(dāng)盈余過(guò)程達(dá)到一個(gè)負(fù)值時(shí)就立刻宣布破產(chǎn);另一方面是關(guān)于分紅支付的確定.通常的分紅是當(dāng)盈余過(guò)程超過(guò)一個(gè)特定的臨界值時(shí),分紅就會(huì)發(fā)生.但是,從實(shí)際的角度來(lái)看,這種決策制定的體制是不太合理的.為了解決這個(gè)問(wèn)題,一些學(xué)者引入了金融學(xué)中的“Parisian延遲”的概念.因“Parisian延遲”允許決策的執(zhí)行有一定的延期,所以使得破產(chǎn)理論中的一些概念更加貼近現(xiàn)實(shí).Parisian概念一般被用到以下兩個(gè)不同的方面.一方面把“Parisian延遲”應(yīng)用于破產(chǎn),從而得到Parisian破產(chǎn)時(shí)間.在這種定義下,只有當(dāng)盈余過(guò)程連續(xù)為負(fù)值的時(shí)間超過(guò)規(guī)定時(shí)間,才考慮宣布破產(chǎn).另一方面把“Parisian延遲”應(yīng)用于分紅,引出了 Parisian分紅時(shí)間.在這種定義下,只有盈余過(guò)程連續(xù)地在一特定的臨界值之上的時(shí)間超過(guò)規(guī)定時(shí)間,才考慮進(jìn)行分紅.本論文研究的主要問(wèn)題是:對(duì)偶風(fēng)險(xiǎn)模型的首次Parisian分紅時(shí)間及對(duì)偶風(fēng)險(xiǎn)模型在破產(chǎn)前進(jìn)行Parisian分紅的問(wèn)題.本論文的結(jié)構(gòu)如下:第一章是緒論及模型介紹.這一章分為三部分,第一部分主要介紹了對(duì)偶風(fēng)險(xiǎn)模型及“Parisian延遲”的發(fā)展歷程;其余兩部分分別介紹了經(jīng)典風(fēng)險(xiǎn)模型以及對(duì)偶風(fēng)險(xiǎn)模型.第二章分析了經(jīng)典風(fēng)險(xiǎn)模型與對(duì)偶風(fēng)險(xiǎn)模型之間的關(guān)系并通過(guò)經(jīng)典風(fēng)險(xiǎn)模型的Parisian破產(chǎn)時(shí)間的Laplace變換給出了對(duì)偶風(fēng)險(xiǎn)模型的首次Parisian分紅時(shí)間的Laplace 變換.第三章分為兩個(gè)部分,分別從兩個(gè)角度研究了對(duì)偶風(fēng)險(xiǎn)模型在破產(chǎn)前進(jìn)行Parisian分紅的概率.第一部分,給出一個(gè)破產(chǎn)概率的廣義的矩母函數(shù)hd(u).不難發(fā)現(xiàn),當(dāng)r=1,δ=0時(shí),hd(u)為初值為u的對(duì)偶風(fēng)險(xiǎn)模型在Parisian分紅前破產(chǎn)的概率,而1 - hd(u)為對(duì)偶風(fēng)險(xiǎn)模型在破產(chǎn)前進(jìn)行Parisian分紅的概率.在論文中得到了hd(u)所滿足的積分微分方程以及當(dāng)收入分布為指數(shù)分布或混合指數(shù)分布時(shí),hd(u)的表達(dá)式;第二部分我們從另一個(gè)方面考慮,給出了首次Parisian延遲分紅時(shí)刻的矩母函數(shù)Vδ(u; b).當(dāng)δ = 0時(shí),Vδ(u;b)為初值為u的對(duì)偶風(fēng)險(xiǎn)模型在破產(chǎn)前進(jìn)行Parisian分紅的概率.同樣地,得到了Vδ(u;b)所滿足的積分微分方程以及當(dāng)收入分布為指數(shù)分布或混合指數(shù)分布時(shí),Vδ(u;b)的表達(dá)式.
[Abstract]:In the papers on bankruptcy, the general custom is to make a direct assessment. For example, with regard to the determination of the time of bankruptcy, bankruptcy is declared immediately when the surplus process reaches a negative value; on the other hand, the determination of dividend payments. The usual dividend is when the surplus process exceeds a specific threshold, the dividend occurs. However, from a practical point of view, this system of decision-making is not very reasonable. To solve this problem, some scholars have introduced the concept of "Parisian delay" in finance. Because "Parisian delay" allows decision execution to be delayed to some extent, some concepts in bankruptcy theory are generally used in the following two different aspects. On the one hand, the "Parisian delay" is applied to the bankruptcy to obtain the Parisian bankruptcy time. Under this definition, a bankruptcy declaration is considered only if the surplus process continues to be negative for longer than the specified time. On the other hand, the Parisian delay is applied to the dividend, which leads to the Parisian dividend time. Under this definition, dividends are considered only if the surplus process continuously exceeds a specified critical value for a specified period of time. The main problems of this thesis are: the first Parisian dividend time of dual risk model and the Parisian dividend of dual risk model before bankruptcy. The structure of this thesis is as follows: the first chapter is introduction and model introduction. This chapter is divided into three parts. The first part mainly introduces the dual risk model and the development of "Parisian delay", and the other two parts introduce the classical risk model and dual risk model respectively. In chapter 2, the relationship between the classical risk model and the dual risk model is analyzed, and the Laplace transformation of the first Parisian dividend time of the dual risk model is given by the Laplace transformation of the Parisian ruin time of the classical risk model. The third chapter is divided into two parts. We study the probability of Parisian dividend in dual risk model before bankruptcy from two angles. In the first part, a generalized moment generating function of ruin probability is given. It is not difficult to find that the dual risk model with initial value u is the probability of ruin before the Parisian dividend, and the dual risk model is the probability of Parisian dividend before the ruin of the dual risk model when r = 1, 未 = 0. In this paper, we obtain the expression of the integro-differential equation satisfied by hddu) and the expression of the income distribution when the income distribution is exponential distribution or mixed exponential distribution. In the second part, we consider another aspect. In this paper, the moment generating function of the first Parisian delay dividend moment is given. When 未 = 0, the probability of Parisian dividend is obtained for the dual risk model with initial value of u when 未 = 0. Similarly, the integro-differential equations satisfied by V 未 U B) and the expressions of V 未 u B) when the income distribution is exponential distribution or mixed exponential distribution are obtained.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：F224;F272

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 成世學(xué);破產(chǎn)論研究綜述[J];數(shù)學(xué)進(jìn)展;2002年05期

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本文編號(hào)：1891371