| dc.contributor.advisor | 許順吉 | zh_TW |
| dc.contributor.advisor | Sheu, Shuenn-Jyi | en_US |
| dc.contributor.author (Authors) | 潘柏樺 | zh_TW |
| dc.contributor.author (Authors) | Pan, Po-Hua | en_US |
| dc.creator (作者) | 潘柏樺 | zh_TW |
| dc.creator (作者) | Pan, Po-Hua | en_US |
| dc.date (日期) | 2023 | en_US |
| dc.date.accessioned | 9-Mar-2023 18:12:58 (UTC+8) | - |
| dc.date.available | 9-Mar-2023 18:12:58 (UTC+8) | - |
| dc.date.issued (上傳時間) | 9-Mar-2023 18:12:58 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0109751008 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/143720 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 109751008 | zh_TW |
| dc.description.abstract (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。 | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | Chapter 1 Introduction 1Chapter 2 The Risk Model and Ruin Probability 3Section 2.1 The Classical Cramér-Lundberg Model Risk Model 3Section 2.2 The Ruin Probability 5Section 2.3 Upper Bound of the Ruin Probability 7Chapter 3 Reinsurance Strategies 11Chapter 4 Optimal Proportional Reinsurance Strategy under Classic Cramér-Lundberg Risk Model 14Section 4.1 HJB Formulation 16Section 4.2 Solution of the HJB equation 18Section 4.3 Verification Theorem 24Chapter 5 Optimal Proportional Reinsurance Strategy under Diffusion Approximation Model 27Section 5.1 Diffusion Approximation of Cramér-Lundburg Process 28Section 5.2 Properties of Controlled Ruin Probability under Diffusion Approximation Model 30Section 5.3 HJB Formulation 35Section 5.4 Solution of the HJB equation 38Section 5.5 Verification Theorem 41Chapter 6 Numerical Results 44Section 6.1 Path Simulation and the Monte Carlo Method 44Section 6.2 Estimation of the Ruin Probability in Finite Time Interval 46Section 6.3 Conclusions 52Bibliography 53Appendix A Lévy Process and Strong Markov Property 54 | zh_TW |
| dc.format.extent | 1347386 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0109751008 | en_US |
| dc.subject (關鍵詞) | 部分再保險 | zh_TW |
| dc.subject (關鍵詞) | 隨機控制 | zh_TW |
| dc.subject (關鍵詞) | 隨機過程 | zh_TW |
| dc.subject (關鍵詞) | 哈密頓-雅可比-貝爾曼方程式 | zh_TW |
| dc.subject (關鍵詞) | Proportional reinsurance | en_US |
| dc.subject (關鍵詞) | Stochastic control | en_US |
| dc.subject (關鍵詞) | Stochastic process | en_US |
| dc.subject (關鍵詞) | HJB equation | en_US |
| dc.title (題名) | Crámer-Lundberg 風險模型及其擴散近似之最適再保險策略 | zh_TW |
| dc.title (題名) | Optimal Proportional Reinsurance Strategies for Classical Crámer-Lundberg Risk Model and It’s Corresponding Diffusion Approximations | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (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, ScandinavianActuarial Journal, 1977:sup1, 37-52.[4] Donald L. Iglehart (1969): Diffusion Approximations in Collective Risk Theory, Journalof 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. | zh_TW |
