| 研究生: |
林晏瑜 Yen-Yu Lin |
|---|---|
| 論文名稱: |
隨機模型情境抽樣有效性之應用 The Application of Efficient Stochastic Modeling from Scenario Sampling |
| 指導教授: |
許玉生
Yu-Sheng Hsu 楊曉文 Sheau-Wen Yang |
| 口試委員: | |
| 學位類別: |
碩士 Master |
| 系所名稱: |
理學院 - 數學系 Department of Mathematics |
| 論文出版年: | 2018 |
| 畢業學年度: | 106 |
| 語文別: | 中文 |
| 論文頁數: | 50 |
| 中文關鍵詞: | 抽樣方法 、情境抽樣 、隨機現金流量測試 |
| 外文關鍵詞: | sampling method, scenario sampling, stochastic cash flow testing |
| 相關次數: | 點閱:17 下載:0 |
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在保險業中我們經常需要做隨機模型情境的模擬,藉由過去的數據來模擬分析未來發生的所有可能性,並進行現金流量分析,然而因龐大的模擬次數,現金流量測試大量的運算時間成為了一項很大的挑戰。因此為了解決大量運行時間的問題,本研究利用不同抽樣方法在不減其模型有效性下減少樣本情境數。本文首先以幾何布朗運動模擬出一百萬組股價報酬的情境,再建立三種不同抽樣方法分別進行抽樣,檢視這三種抽樣方法是否能夠有效減少模型運行次數,並比較三種抽樣方式的優劣,且同時檢驗抽樣後隨機模型的有效性。最後本研究將抽樣結果實際應用在隨機現金流量測試中,利用條件尾端期望值作為標準,對保單責任準備金的適足性進行測試,來達到運用抽樣方法減少情境次數同時大幅減少現金流量測試責任準備金適足性運行時間的目的。
In the insurance industry, simulations of stochastic model scenarios are frequently used to simulate and analyze future possibilities with data in the past and conducted in cash flow testing. However, due to the huge number of simulation times, long time of computing cash flow testing becomes a big challenge. Therefore, to solve the problem of long computing time, this research reduces the number of scenario with different sampling methods but under the premises that no efficiency of models would be affected. In this paper, we use geometric Brownian motion to simulate scenarios for ten thousand groups of stock price return, and then we build three different sampling methods to check the efficiency of stochastic modeling from scenario sampling. Finally, we apply the sampling result to the stochastic cash flow testing. In addition, we use conditional tail expectation as a standard to test the adequacy of policy reserve and thus to reduce scenario times, and at the same time, to reduce cash flow testing time by using scenario sampling.
1. Edward L. Robbins, Samuel H. Cox and Richard D. Phillips (1997), Application of Risk Theory to Interpretation of Stochastic Cash-Flow-Testing Results, 85-98
2. Yvonne C. M. Chueh (2002), Efficient Stochastic Modeling for Large and Consolidated Insurance Business:Interest Rate Sampling Algorithms, 88-103.
3. Yvonne C. M. Chueh (2003), Efficient Stochastic Modeling from Scenario Sampling To Parametric Model Fitting Utilizing ASEM as an Example.
4. David C. M. Dickson, Mary R. Hardy and Howard R. Waters (2013), Actuarial Mathematics for Life Contingent Risks. Cambridge, 397-407.
5. Black, Fischer, and Myron Scholes (1973), The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, 637-654.
6. Michael G. Hilgers (2000), Quasi-Monte Carlo methods in cash flow testing simulations, 517-526
7. 李綾(2006), 隨機模型建構在保險業現金流量測試之應用, 國立中央大學, 財務金融學碩士論文。
8. 詹惟淳(2013), 考慮保戶行為下對附保證投資型商品準備金之評估, 國立中央大學, 財務金融學碩士論文。
9. 黃克崴(1998), 隨機投資模型在精算上的應用, 私立東吳大學, 商用數學碩士論文。