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研究生: 石異呈
YI-CHENG SHIS
論文名稱: 複合卜瓦松過程在具交互影響的投資案資源分配問題
An Application of Compound Poisson Process to resource allocation problem with interaction affect 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: 38
中文關鍵詞: 風險理論模型複合卜瓦松過程安全負荷係數資源分配
外文關鍵詞: Risk theory model, Compound Poisson Process, Security loading value, Resources distribution
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  • 本文中,我們將採用複合卜瓦松過程來討論兩個在具有交互影響的投資案下資源分配的問題。除了引用風險理論經典模型的理念,也參考一些資源如何分配的方法,並以更廣的角度來看待每個可能發生的情形,再舉出虛擬例子來創立模型並解決問題,最後以數值範例,討論出更好的投資組合策略。


    In this paper, we will use the Compound Poisson Process theory to discuss the resources distribution problem for the two investments with interactive affections to each other. In addition to the concept of the classical model in risk theory,we also made reference to the ways how to allocate the resource,and look at every possible situation with a broader perspective point of view. Then by citing the virtual example, model will be created and shown the solving of the problems. Finally,by numerical examples,we will discuss and come out a better portfolio strategy for investment.

    摘要(中文)--------------------------------------------------I 摘要(英文)-------------------------------------------------II 目錄-----------------------------------------------------III 圖目錄----------------------------------------------------IV 第一章 緒論----------------------------------------------1 第二章 文獻探討-------------------------------------------3 第三章 模型的假設與應用------------------------------------6 3-1 模型建構------------------------------------------6 3-2 模型性質-----------------------------------------10 第四章 數值範例------------------------------------------21 第五章 結論------------------------------------------------31 參考文獻---------------------------------------------------32 附錄------------------------------------------------------33

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    [2] 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.
    [3] 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.
    [4] 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.
    [5] Durrett R.(2010), “Probability Theory and Examples fourth Edition”,Cambridge Univ P
    [6] 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.
    [7] Ross S.M.(1996),“Stochastic processes second edition”, John Wiley & Sons Inc

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