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    题名: Crámer-Lundberg 風險模型及其擴散近似之最適再保險策略
    Optimal Proportional Reinsurance Strategies for Classical Crámer-Lundberg Risk Model and It’s Corresponding Diffusion Approximations
    作者: 潘柏樺
    Pan, Po-Hua
    贡献者: 許順吉
    Sheu, Shuenn-Jyi
    潘柏樺
    Pan, Po-Hua
    关键词: 部分再保險
    隨機控制
    隨機過程
    哈密頓-雅可比-貝爾曼方程式
    Proportional reinsurance
    Stochastic control
    Stochastic process
    HJB equation
    日期: 2023
    上传时间: 2023-03-09 18:12:58 (UTC+8)
    摘要: 再保險是保險公司管理風險的有力工具。如果我們將保險公司隨時間變化的淨利潤建模為一個隨機過程，將再保險策略視為一個控制過程，那麼最小化這種隨機過程的破產機率就是一個隨機控制問題。本文旨在尋找最適再保險策略，使破產機率最小化。與許多其他隨機控制問題一樣，我們使用哈密頓-雅可比-貝爾曼方程來求解該問題。
    Reinsurance is a powerful tool for insurance company to manage the risk. If we model the net profit of insurance company over time as a stochastic process and view the reinsurance strategy as a control process, then to minimize the ruin probability of such stochastic process is a stochastic control problem. This article aims to find the optimal reinsurance strategy so that the ruin probability to be minimized. As many other stochastic control problem, we use the Hamilton-Jacobi-Bellman (HJB) equation to solve the problem.
    參考文獻: [1] Hanspeter Schmidli (2007): Stochastic Control in Insurance, 2007.
    [2] Hanspeter Schmidli (2017): Risk Theory, 2017.
    [3] Jan Grandell (1977): A class of approximations of ruin probabilities, Scandinavian
    Actuarial Journal, 1977:sup1, 37-52.
    [4] Donald L. Iglehart (1969): Diffusion Approximations in Collective Risk Theory, Journal
    of Applied Probability, 1969: 285-289.
    [5] Bernt Øksendal (2000): Stochastic Differential Equations, 2000.
    [6] Jean-François Le Gall (2016): Brownian motion, Martingales, and Stochastic Calculus,
    2016.
    [7] Jean Jacod, Philip Protter (2004): Probability Essential, 2004.
    描述: 碩士
    國立政治大學
    應用數學系
    109751008
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0109751008
    数据类型: thesis
    显示于类别:[應用數學系] 學位論文

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