請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69119
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 韓傳祥 | |
dc.contributor.author | Dung-Cheng Lin | en |
dc.contributor.author | 林東成 | zh_TW |
dc.date.accessioned | 2021-06-17T03:09:23Z | - |
dc.date.available | 2019-07-24 | |
dc.date.copyright | 2018-07-24 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-07-23 | |
dc.identifier.citation | [1] Viral Acharya, Robert Engle, and Matthew Richardson. “Capital shortfall: A new approach to ranking and regulating systemic risks”. In: The American Economic Review 102.3 (2012), pp. 59–64.
[2] Viral Acharya et al. “Measuring systemic risk”. In: The Review of Financial Studies 30.1 (2017), pp. 2–47. [3] Tobias Adrian and Markus K Brunnermeier. “CoVaR”. In: The American Economic Review 106.7 (2016), pp. 1705–1741. [4] Jan Baldeaux and Eckhard Platen. Functionals of multidimensional diffusions with applications to finance. Vol. 5. Springer Science & Business Media, 2013. [5] James Bucklew. Introduction to rare event simulation. Springer Science & Business Media, 2013. [6] René Carmona, Jean-Pierre Fouque, and Douglas Vestal. “Interacting particle systems for the computation of rare credit portfolio losses”. In: Finance and Stochastics 13.4 (2009), pp. 613–633. [7] Y.-A. Chen. “Importance Sampling for Estimating High Dimensional Joint Default Probabilities”. MA thesis. http://dx.doi.org/10.6342/NTU201702908: National Tai- wan University, July 2017. [8] Umberto Cherubini, Elisa Luciano, and Walter Vecchiato. Copula methods in finance. John Wiley & Sons, 2004. [9] Amir Dembo and Ofer Zeitouni. Large deviations techniques and applications, volume 38 of Stochastic Modelling and Applied Probability. 2010. [10] Darrell Duffie and Kenneth J Singleton. Credit risk: pricing, measurement, and management. Princeton University Press, 2012. [11] Robert Engle. Anticipating correlations: a new paradigm for risk management. Princeton University Press, 2009. [12] L.C. Evans. Partial Differential Equations. Graduate studies in mathematics. American Mathematical Society, 2010. ISBN: 9780821849743. [13] Jean-Pierre Fouque and Joseph A Langsam. Handbook on systemic risk. Cambridge University Press, 2013. [14] Alan Genz and Frank Bretz. “Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts”. In: Journal of Statistical Computation and Simulation 63.4 (1999), pp. 103–117. [15] Paul Glasserman. Monte Carlo methods in financial engineering. Vol. 53. Springer Science & Business Media, 2013. [16] Paul Glasserman, Philip Heidelberger, and Perwez Shahabuddin. “Portfolio value- at-risk with heavy-tailed risk factors”. In: Mathematical Finance 12.3 (2002), pp. 239– 269. [17] Paul Glasserman, Philip Heidelberger, and Perwez Shahabuddin. “Variance reduction techniques for estimating value-at-risk”. In: Management Science 46.10 (2000), pp. 1349–1364. [18] Chuan-Hsiang Han. “Efficient importance sampling estimation for joint default probability: The first passage time problem”. In: Stochastic Analysis with Financial Applications (Proceedings of 2009 Workshop on Stochastic Analysis & Finance). Vol. 65. Springer. 2011, pp. 409–418. [19] Chuan-Hsiang Han, Wei-Han Liu, and Tzu-Ying Chen. “VaR/CVaR estimation under stochastic volatility models”. In: International Journal of Theoretical and Applied Finance 17.02 (2014), p. 1450009. [20] John C Hull and Sankarshan Basu. Options, futures, and other derivatives. Pearson Education India, 2016. [21] Philippe Jorion. Value at risk: the new benchmark for controlling market risk. Irwin Professional Pub., 1997. [22] Philippe Jorion. Value at risk: The new benchmark for managing market risk. 2000. [23] Benjamin Jourdain, Jérôme Lelong, et al. “Robust adaptive importance sampling for normal random vectors”. In: The Annals of Applied Probability 19.5 (2009), pp. 1687–1718. [24] David Lando. Credit risk modeling: theory and applications. Princeton University Press, 2009. [25] Paul Malliavin, Maria Elvira Mancino, et al. “A Fourier transform method for non- parametric estimation of multivariate volatility”. In: The Annals of Statistics 37.4 (2009), pp. 1983–2010. [26] Michel Mandjes. Large deviations for Gaussian queues: modelling communication networks. John Wiley & Sons, 2007. [27] Alexander J McNeil, Rüdiger Frey, and Paul Embrechts. Quantitative risk management: Concepts, techniques and tools. Princeton university press, 2015. [28] Monte Carlo and Quasi-Monte Carlo Sampling. Springer, 2009. [29] Bernt Øksendal. “Stochastic differential equations”. In: Stochastic differential equations. Springer, 2003, pp. 65–84. [30] Qi-Man Shao. “A Cramér type large deviation result for Student’s t-statistic”. In: Journal of Theoretical Probability 12.2 (1999), pp. 385–398. [31] WT Shaw and KTA Lee. “Bivariate Student t distributions with variable marginal degrees of freedom and independence”. In: Journal of Multivariate Analysis 99.6 (2008), pp. 1276–1287. [32] Cathrin Van Emmerich. “Modelling correlation as a stochastic process”. In: preprint 6.03 (2006). | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69119 | - |
dc.description.abstract | 在風險管理的領域,多變數的分佈時常被用來測量一個系統內多個單位同時的違約機率。重要抽樣法時常被用來當作稀有事件的模擬。在常態分佈的假設下,我們證明了文中所給定的重要抽樣法對於矩陣值隨機的左尾端機率估計是漸進最佳的。在與其他的演算法比較下可以發現其優勢。此外,這樣的方法也可以拿來估計體系風險的問題。 | zh_TW |
dc.description.abstract | In view of risk management, the tail probability of a multivariate distribution is a basic quantity to measure the occurrence of events that several components of a system collapse simultaneously. Importance sampling is commonly used for rare event simulation. Given the Gaussian distribution, we prove that our proposed importance sampling scheme is asymptotically optimal for matrix valued normal distributions and Brownian motions. Numerical comparisons with some commercial algorithm demonstrate superior of our proposed method. The importance sampling scheme can also be to study the systemic risk estimation. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T03:09:23Z (GMT). No. of bitstreams: 1 ntu-107-R05246004-1.pdf: 7565484 bytes, checksum: 9d4a540dce6ba27421422232a8114529 (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | 誌謝 v
摘要 vii Abstract ix 1 Introduction 1 2 Matrix Valued Stochastics 3 2.1 Matrix Valued Normal Distribution 4 2.2 Matrix Valued Brownian Motion 4 3 Large Deviation Theory 7 3.1 Cramer's theorem 8 3.2 Large Deviation Principle for Sample Path 10 4 Efficient Importance Sampling Scheme for Matrix Valued Normal Distributions 13 4.1 Importance Sampling Scheme 13 4.2 Asymptotic Variance Analysis by Large Deviation Principle 16 4.3 Numerical Results 18 5 Efficient Importance Sampling Scheme for Matrix Valued Brownian Motions 21 5.1 Importance Sampling Scheme 22 5.2 Asymptotic Variance Analysis by Large Deviation Principle 23 6 Application: Systemic Risk in Finance 31 6.1 Systemic Risk Measures: SRISK, ΔCoVaR 31 6.1.1 Construction of Importance Sampling Scheme for SRISK 32 6.1.2 Construction of Importance Sampling Scheme for ΔCoVaR 33 7 Conclusion 41 Bibliography 43 | |
dc.language.iso | en | |
dc.title | 在矩陣值隨機下對左尾端機率估計的漸進最佳重要抽樣法 | zh_TW |
dc.title | Asymptotically Optimal Importance Sampling for Lower Tail Probability Estimation under Matrix Valued Stochastics | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 許順吉,張志中 | |
dc.subject.keyword | 重要抽樣法,漸進最佳,矩陣值隨機,體系風險, | zh_TW |
dc.subject.keyword | importance sampling,asymptotic optimality,matrix valued stochastics,systemic risk, | en |
dc.relation.page | 45 | |
dc.identifier.doi | 10.6342/NTU201801756 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2018-07-23 | |
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-107-1.pdf 目前未授權公開取用 | 7.39 MB | 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。