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研究生: 許燕妮
YEN-NI HSU
論文名稱: 複合卜瓦松過程在投資案的資源分配問題
An Application of Compound Poisson Process to Resource Allocation Problem in the Investment Proposal
指導教授: 洪文良
Wen-Liang Hung
張延彰
Yen-Chang Chang
口試委員:
學位類別: 碩士
Master
系所名稱: 南大校區系所調整院務中心 - 應用數學系所
應用數學系所(English)
論文出版年: 2012
畢業學年度: 100
語文別: 中文
論文頁數: 36
中文關鍵詞: 風險理論模型複合卜瓦松過程期望值安全負荷係數資源分配
外文關鍵詞: Risk theory model, Compound Poisson Process, Expected value, Security loading value, Resources distribution
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  • 本文主要是引用風險理論模型的概念,利用複合卜瓦松過程來討論投資案的資源分配問題。我們考慮同時進行兩筆投資案和三筆投資案的模型及應用,並討論出投資案的最佳方法,得知最大期望獲益及其風險,最後用數值範例說明並驗證。


    In this paper, We introduce to the concept of model of risk theory, and we use the Compound Poisson Process to discuss the investment resource allocation problem.
    We consider the model to the two proposal of investments , and three proposal of investments the best way come out by discussion for the investment proposal,showing the maximum expected benefit from their risk, and finally numerical examples to illustrate and justify.

    摘要(中文)--------------------------------------------------I 摘要(英文)-------------------------------------------------II 目錄-----------------------------------------------------III 第一章 緒論----------------------------------------------1 第二章 文獻探討-------------------------------------------3 第三章 模型假設與探討--------------------------------------6 3.1 二筆投資案模型的假設-------------------------------------6 3.2 二筆投資案模型的應用-------------------------------------7 3.3 二筆投資案的安全負荷係數---------------------------------11 3.4 三筆投資案模型的假設------------------------------------12 3.5 三筆投資案模型的應用------------------------------------13 3.6 三筆投資案的安全負荷係數---------------------------------18 第四章 數值範例------------------------------------------19 4.1二筆投資案的數值範例-------------------------------------19 4.2 二筆投資案的破產機率------------------------------------21 4.3 當破產機率門檻大於零------------------------------------22 4.4 三筆投資案的數值範例------------------------------------24 4.5三筆投資案的破產機率-------------------------------------27 4.6當破產機率門檻大於零-------------------------------------28 第五章 結論------------------------------------------------30 參考文獻---------------------------------------------------31 附錄------------------------------------------------------32

    [1] Cai J. and Yang H.(2005),“Ruin in the perturbed compound Poisson risk process
    under interest force”,Advances in Applied Probability, vol.37,pp.819-835.
    [2] Dickson D.C.M. and Waters H.R.(2002),“The distribution of the time to ruin in the classical risk model”,Astin Bulletin,vol.32, pp.299-313.
    [3] Dufresne F. and Gerber H.U.(1991),“Risk theory for the compound Poisson
    Process that is perturbed by diffusion”,Insurance: Mathematics and Economics,
    10(1),pp.51-59.
    [4] Durrett R.(2010),“Probability Theory and Examples fourth Edition”,
    Cambridge Univ Pr
    [5] Forman E.H. and Selly M.A.(2002), “Decision by objectives: How to convince
    others that you are right”,World Scientific Pub Co Inc, pp235-289.
    [6] Ross S.M.(1996),“Stochastic processes second edition”,John Wiley & Sons Inc

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