Workshop on Advanced Probability and Statistics
School of Mathematical Sciences, Soochow University
Suzhou 215006, China
Nov. 8, 2018
Schedule of the Workshop
Thursday, November 8, 2018
F2 Conference Room, Jing-Zheng Building, Main Campus, Soochow University
09:00--10:00 Registration
10:00--10:40 Dr Giovanni Merola (Xi’an Jiaotong-liverpool Uiversity)
New developments in sparse principal component analysis
10:40--11:20 Dr Jiajun Liu (Xi’an Jiaotong-liverpool Uiversity)
Asymptotics for Systemic Risk with Dependent Heavy-tailed Losses
11:20--12:00 Dr Jigao Yan (Soochow University)
On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables
12:00--13:30 Lunch at Dong-Wu Restaurant
13:30--14:10 Dr Lu Zong (Xi’an Jiaotong-liverpool Uiversity)
Financial Early Warning System for Chinese Stock Market based on Long and Short Term Memory Neural Networks
14:10--14:50 Dr Hasanjan Sayit (Xi’an Jiaotong-liverpool Uiversity)
Martingale measures in markets with proportional transaction costs
14:50--15:30 Dr Zaichao Du (Soochow University)
Modeling Systemic Risk --- A DCC-Filtered Historical Simulation Approach
15:30--17:00 Campus walk / Free discussion
17:00--18:30 Dinner at Dong-Wu Restaurant
New developments in sparse principal component analysis (Dr Giovanni Merola)
Abstract: Sparse methods are becoming more and more important in statistical learning and analysis. Sparse PCA (SPCA) methods were introduced in the early 00's and a great many different versions have been proposed since then. SPCA is currently used in many fields of application, such as image recognition, linear and nonlinear classification problems, etc. However, the model adopted in these conventional SPCA methods has several drawbacks, the most serious of which is that the sparse components do not maximise the variance explained. I will review a more sound approach to SPCA, based on least squares optimisation, and introduce a related approach, Projection SPCA. I will show how these methods outperform the conventional approach with respect to different criteria. As time permits, I will exemplify how Projection SPCA can be used to compute sparse rotated PCs.
Asymptotics for Systemic Risk with Dependent Heavy-tailed Losses (Dr Jiajun Liu)
Abstract: Systemic risk is considered as the risk of collapse of an entire financial system, which has played a significant role in explaining the recent financial turmoils from the insurance and financial industries. Although there exists a very large number of systemic risk measures in the literature on the Systemic risk (SR), the more simple SR definition from Acharya et al. (2012) is chosen to be discussed. We consider the tail behavior of the Systemic risk (SR) for portfolio losses. We generalize the model to allow for heavy-tailed distribution of risk factors, which are equipped with a wide type of dependence structure. For various important cases, asymptotic formulas for the SR are derived. This risk model provides an ideal framework for modeling both heavy tails and dependence.
As an extension, simulation experiments are conducted, comparing the asymptotic formulas with the traditional empirical estimators, which show that our approach is superior to an empirical approach.
On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables (Dr Jigao Yan)
Abstract: We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions. Consequently, we get the result for many dependent structure, such as END, $/varrho^*$-mixing, $/varrho^{-}$-mixing and $/varphi$-mixing, etc.
Financial Early Warning System for Chinese Stock Market based on Long and Short Term Memory Neural Networks (Dr Lu Zong)
Abstract: In this study, the long and short term memory (LSTM) network is applied for the purpose of constructing a financial crisis early-warning system (EWS) to monitor and predict price turmoils in the Chinese stock market. By classifying the price series into high (implying crisis) and low (implying non-crisis) volatility states, it allows us to formulate the crisis EWS model into a binary-classfication problem of two levels: (i) the application of the LSTM model on the stock price series by introducing macro-economic factors and varying classified crisis thresholds without breaking the innate property of time; (ii) the estimation and selection of feature importance according to the predicting Rand accuracy and the Binary cross entropy loss ratio. To validate the forecasting power of our proposed model, we compare it with the backpropagation neural network (BPNN) by adopting both models on the weekly stock data of China during the period of Yr:1990-2018. Main conclusions can be extracted as (i) LSTM successfully seizes the stock price break down that took place at the mid-year of 2015, and alarms the forthcoming shock in the most recent October of 2018; (ii) the proposed EWS model based on the LSTM evidently outperforms the BPNN-based model with a stronger forecasting power; (iii) macro-economic factors such as M1, M2 and CPI contribute to the model performance in terms of both the forecasting effectiveness or accuracy.
Martingale measures in markets with proportional transaction costs (Dr Hasanjan Sayit)
Abstract: consistent price systems (CPSs) play the role of martingale measures in financial markets with proportional transaction costs. We introduce a sufficient condition for the existence of CPSs for jump processes. Existence of CPS for strict local martingale will also be discussed.
Modeling Systemic Risk --- A DCC-Filtered Historical Simulation Approach (Dr Zaichao Du)
Abstract: This paper proposes a DCC-filtered historical simulation approach to modeling systemic risk. We explain our method in terms of CoVaR and CoES (Adrian and Brunnermeie 2016), and show its applicability to Marginal Expected Shortfall (MES) and SRISK. We also propose unconditional and conditional backtests for CoES by extending the tests in Du and Escanciano (2017). Empirical applications to U.S. financial markets highlight the merits of our method.