請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67056
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 韓傳祥 | |
dc.contributor.author | Yen-An Chen | en |
dc.contributor.author | 陳彥安 | zh_TW |
dc.date.accessioned | 2021-06-17T01:18:38Z | - |
dc.date.available | 2020-08-25 | |
dc.date.copyright | 2017-08-25 | |
dc.date.issued | 2017 | |
dc.date.submitted | 2017-08-11 | |
dc.identifier.citation | [1] V. Acharya, R. Engle, and M. Richardson. Capital shortfall: A new approach to ranking and regulating systemic risks. The American Economic Review, 102(3):59– 64, 2012.
[2] J. Bucklew. Introduction to rare event simulation. Springer Science & Business Media, 2013. [3] R. Carmona, J.-P. Fouque, and D. Vestal. Interacting particle systems for the com- putation of rare credit portfolio losses. Finance and Stochastics, 13(4):613–633, 2009. [4] A. Dembo and O. Zeitouni. Large deviations techniques and applications, vol- ume 38. Springer Science & Business Media, 2009. [5] P. Dupuis and R. S. Ellis. A weak convergence approach to the theory of large deviations, volume 902. John Wiley & Sons, 2011. [6] M. Fischer et al. On the form of the large deviation rate function for the empirical measures of weakly interacting systems. Bernoulli, 20(4):1765–1801, 2014. [7] A. Friedman. Variational principles and free-boundary problems. Courier Corpora- tion, 2010. [8] P. Glasserman. Monte Carlo methods in financial engineering, volume 53. Springer Science & Business Media, 2013. [9] P. Glasserman, P. Heidelberger, and P. Shahabuddin. Variance reduction techniques for estimating value-at-risk. Management Science, 46(10):1349–1364, 2000. 42 [10] S. Iyengar. Hitting lines with two-dimensional brownian motion. SIAM Journal on Applied Mathematics, 45(6):983–989, 1985. [11] S. Kou and H. Zhong. First-passage times of two-dimensional brownian motion. Advances in Applied Probability, 48(4):1045–1060, 2016. [12] E. Platen and R. Rendek. Exact scenario simulation for selected multi-dimensional stochastic processes. 2009. [13] S. S. Varadhan et al. Large deviations. The annals of probability, 36(2):397–419, 2008. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67056 | - |
dc.description.abstract | 我們探討估計稀有事件機率的模擬方法,特別針對「聯合違約」事 件於不同模型中的狀況。我們所提供的方法主要基於重要抽樣法,是 一種藉由增加抽到稀有事件的比率,來減低抽樣誤差的技術。本篇論 文主要分為兩部分。在第一部分,我們提出在四個不同模型下,決定 重要抽樣法機率測度的方式。其中,這些方法引入大離差理論的結果, 可以被證明是「漸進式最佳」的。此外,大部分模型在高維度狀況並 不擁有解析解,而我們的結果皆適用在多維度的情形。第二部分,我 們將先前的結果拿來應用在更為複雜的模型上,可以看到在幾個例子, 皆有出色的數值成果,同時計算上仍保持一定效率。 | zh_TW |
dc.description.abstract | We discuss the simulation method for estimating the probabilities of rare events, especially the “joint default” probabilities under different models. The methods we provide are based on importance sampling, which is a variance re- duction technique used to increase the number of samples reaching the “rare” region. There are two parts in this thesis. For the first part, we provide several importance sampling schemes, where the “asymptotically optimal” (or efficient) property is proved by applying the large deviation theory. Also, the results could be applied to the multi-dimensional scene, where most of the probabilities interested do not have an explicit expression. For the second part, we apply our idea to the model that is more complicated. It is shown that we have some satisfying results while keeping the computation efficient. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T01:18:38Z (GMT). No. of bitstreams: 1 ntu-106-R03246004-1.pdf: 383404 bytes, checksum: 64761ca6da079f7ea6555745aa6d2cde (MD5) Previous issue date: 2017 | en |
dc.description.tableofcontents | 摘要 i
Abstract ii 1 Introduction 1 2 Large Deviation Theory 4 2.1 Cramer Theorem (Multivariate) ...................... 5 2.2 Schilder’sTheorem............................. 5 3 Efficient Importance Sampling Schemes for Joint Default Events 8 3.1 Multivariate Normal Distribution...................... 8 3.2 Brownian Motionabove Deterministic Function ............. 14 3.3 Multi Dimensional Correlated Brownian Motion - First Passage Time Problem ..................................... 21 3.4 Multi Dimensional Geometric Brownian Motion - First Passage Time Problem ..................................... 27 4 Topics on Financial Applications 33 4.1 P(F(Wt)>c) ............................... 33 4.2 Systemic risk ................................ 36 5 Conclusion 41 Bibliography 42 | |
dc.language.iso | zh-TW | |
dc.title | 重要抽樣法在估計高維度聯合違約機率的應用 | zh_TW |
dc.title | Importance Sampling for Estimating High Dimensional Joint Default Probabilities | en |
dc.type | Thesis | |
dc.date.schoolyear | 105-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 吳慶堂,許順吉,黃基志 | |
dc.subject.keyword | 聯合違約,稀有事件模擬,高效能重要抽樣法, | zh_TW |
dc.subject.keyword | joint default event,rare event simulation,efficient importance sampling, | en |
dc.relation.page | 43 | |
dc.identifier.doi | 10.6342/NTU201702908 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2017-08-14 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
顯示於系所單位: | 應用數學科學研究所 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-106-1.pdf 目前未授權公開取用 | 374.42 kB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。