Data Analysis and Related Applications 4: New Approaches

Chapter 1. On the First-Passage Area of a One-Dimensional Diffusion Process with Stochastic Resetting
	1.1. Formulation of the problem and general results
	1.2. Brownian motion with resetting
		1.2.1. Moments of the FPT
		1.2.2. Moments of the FPA
		1.2.3. Joint moment of A(x) and t (x)
		1.2.4. Maximum displacement
	1.3. Drifted Brownian motion with resetting
		1.3.1. The Laplace transform of t (x)
		1.3.2. Moments of the FPT
		1.3.3. Mean of the FPA
		1.3.4. Maximum displacement
	1.4. References
Chapter 2. Statistical Analysis of Groundwater Level in Slovakia
	2.1. Introduction
	2.2. Data and methods
		2.2.1. Change-point detection methods
		2.2.2. Trend analysis
		2.2.3. Spearman’s rho test
	2.3. Results
	2.4. Conclusion
	2.5. Acknowledgment
	2.6. References
Chapter 3. Stochastic Processes Associated with Fully Nonlinear Parabolic Equations Arising in Financial Mathematics
	3.1. Semilinear and fully nonlinear PDEs
	3.2. BSDE, FBSDE and deep learning algorithms
	3.3. Acknowledgments
	3.4. References
Chapter 4. An Improved Shape Parameter Estimation Method for the Pareto Model
	4.1. Introduction
	4.2. Estimators under study
		4.2.1. Common methods of estimation
		4.2.2. Log-generalized probability weighted moment estimator
	4.3. An algorithm for selection of the control parameter of the LGPWM shape parameter estimator
	4.4. Numerical results
		4.4.1. Simulation study
		4.4.2. Real data analysis
	4.5. Conclusion
	4.6. Acknowledgments
	4.7. References
Chapter 5. BSDE-. Scheme for the Heston Model: Valuation of American Options
	5.1. Background
	5.2. BSDE numerical schemes
		5.2.1. The Heston model
		5.2.2. BSDE representation of the Heston model
		5.2.3. BSDE-. scheme under the Heston model
	5.3. Numerical experimental studies: valuation of American options
	5.4. Conclusion and future work
	5.5. References
Chapter 6. Age-replacement Policy for Series Systems Under Parameter Uncertainty in Lifetime Distribution
	6.1. Introduction
	6.2.The model
		6.2.1. Lifetime of units
		6.2.2. Maintenance action and time
		6.2.3. Maintenance policy
		6.2.4. Cost model and cost rate
	6.3. Optimization
		6.3.1. A special case
	6.4. Numerical example
	6.5. Conclusion
	6.6. References
Chapter 7. New Bicluster Algorithm for Trading
	7.1. Introduction
	7.2. Fuzzy logic and trading rules
	7.3. Sentiment analysis, trading indicators and fuzzy rules
	7.4. Conclusion
	7.5. References
Chapter 8. A Flexible Generalization of the Latent Dirichlet Allocation
	8.1. Introduction
	8.2. Distributions on the simplex
	8.3. Latent topic models
	8.4. Collapsed Gibbs sampling
	8.5. Simulation study
	8.6. References
Chapter 9. Extreme Value Parameters Estimation: An Overview
	9.1. Introduction and overview of extreme value theory
	9.2. Some parameters of interest in EVT
	9.3. EVI and EI estimation
		9.3.1. EVI estimators
		9.3.2. EI estimators
	9.4. Extreme quantile estimation
	9.5. Application to the daily mean flow discharge in river Tejo
	9.6. Conclusion and work in progress
	9.7. Acknowledgments
	9.8. References
Chapter 10. Some Properties on Optimal Maintenance Policies for k-out-of-n:G Systems Considering Imperfect Repair with Controllable Repair Levels
	10.1. Introduction
	10.2. System description
		10.2.1. Deterioration state
		10.2.2. Maintenance actions
	10.3. Total expected discounted cost
	10.4. Optimization of maintenance policy
	10.5. Numerical studies
		10.5.1. Optimal maintenance policies for a two-out-of-three system
		10.5.2. Sensitivity analysis
	10.6. Conclusion
	10.7. References
Chapter 11. Stochastic Orders and Reliability Properties for the Deficit at Ruin and Bounds for the Laplace Transform of a Compound Geometric Distribution
	11.1. Introduction
	11.2. Model description and results
	11.3. Bounds for the LT of the maximal aggregate loss
	11.4. Examples
	11.5. References
Chapter 12. A New Family of Continuous Univariate Distributions with Applications in Actuarial Science
	12.1. Introduction
	12.2. Definitions and notations
	12.3. Probability bounds
	12.4. Aging properties and unimodality
	12.5. Tail behavior of Dg +(h)
	12.6. Conclusion
	12.7. Acknowledgment
	12.8. References
Chapter 13. Simple Form of Probability Density Functions via Sampling
	13.1. Introduction
	13.2. The sense and the method
		13.2.1. The first step
		13.2.2. The second step
	13.3. Using sampling data
	13.4. Results and discussion
	13.5. References
Chapter 14. Optimizing Financial Trading Strategies Using Dynamic Bayesian Networks
	14.1. Introduction
	14.2. Theoretical framework
		14.2.1. Inference for DBNs
		14.2.2. Learning DBNs
		14.2.3. Application of theory
		14.2.4. Inference with known parameters
		14.2.5. Learning unknown parameters
	14.3. Methodology of analysis and results
	14.4. Conclusion
	14.5. References
Chapter 15. Quantitative Methods for Analysing the Risk and Timing of Bankruptcy of Small and Medium Enterprises
	15.1.Introduction
	15.2. Approaches to statistical modeling
	15.3. Imbalanced data
		15.3.1. Estimating the logistic regression model with imbalanced data
		15.3.2. Separate sampling of good and bad units
		15.3.3. Modifying the sample to deal with imbalanced data
	15.4. Competing risks
	15.5. Conclusion
	15.6. References
Chapter 16. Network of Adaptive Frequency Oscillators in a Ballistic, Non-Gaussian, Noisy Environment
	16.1. Introduction
	16.2. Dynamics of the network
	16.3. Analyzing the dynamics
		16.3.1. The effect of the random vector B
		16.3.2. Main results
	16.4. Numerical simulations
	16.5. Discussion and perspectives
	16.6. Appendices
		16.6.1. Appendix 1: Solution of the linear stochastic differential equation
		16.6.2. Appendix 2: Calculations for changing back the variables, expected values and covariance matrices
		16.6.3. Appendix 3: Distributions concerning the random vector B
		16.6.4. Appendix 4: Eigenvalues of the Laplacian matrix of the “All-to-All” network
	16.7. References
Chapter 17. Penalised Regression Adaptations of the Longstaff–Schwartz Algorithm for Pricing American Options
	17.1. Introduction
	17.2. The Longstaff–Schwartz algorithm and proposed extensions
	17.3. Stochastic processes in finance and relevant theoretical considerations
	17.4. Simulation design
	17.5. Results
	17.6. Conclusion
	17.7. References
Chapter 18. International Auditing Standards and Their Contribution to the Limitation of Accounting Fraud
	18.1. Introduction
	18.2. Literature review
		18.2.1. International Auditing Standards
		18.2.2. Accounting fraud – falsification of financial statements
		18.2.3. The Fraud Triangle
		18.2.4. Fraud Diamond
		18.2.5. Detection and prevention of accounting fraud
	18.3. Empirical analysis
		18.3.1. Introduction
		18.3.2. Sample
		18.3.3. Methodology
		18.3.4. Simple linear regression
		18.3.5. Analysis of auditors’ questionnaire data
		18.3.6. Analysis of questionnaire data of large companies
		18.3.7. Comparative analysis of auditors’ and companies’ results
	18.4. Conclusion
	18.5. References
Chapter 19. Equivariant Robust Estimators for Moment Condition Models
	19.1. Introduction
	19.2. Robust estimators for moment condition models
		19.2.1. Statistical divergences
		19.2.2. Definition of the estimators
	19.3. Equivariance of robust minimum empirical divergence estimators
		19.3.1. Groups of transformations, invariant models and equivariant estimators
		19.3.2. Equivariance of robust minimum empirical divergence estimators
	19.4. Acknowledgments
	19.5. References
Chapter 20. Continuous Increasing Probability Density Functions: An Approach Through Sampling
	20.1. Introduction
	20.2. Theoretical approach
	20.3. Examples for illustration
	20.4. Results and discussion
	20.5. References
Chapter 21. The Importance of the Initial Selection of Suppliers in the Food Service Divisions of Hotels, the Current Situation in the Supply Chain of Greece
	21.1. Introduction
	21.2. Literature review
	21.3. Benefits of supply chain management
	21.4. Research methodology
		21.4.1. The questionnaire
	21.5. Data analysis
		21.5.1. Reliability analysis
		21.5.2. Results
	21.6. Discussion
	21.7. Conclusion
	21.8. References
Chapter 22. Compliance with IUU Fisheries of Manila Clams in the Tagus Estuary
	22.1. Introduction
	22.2. Research methodology
	22.3. Analysis and interpretation of results
	22.4. Conclusion
	22.5. Acknowledgments
	22.6. References
Chapter 23. The Expectation of a Mixed Moving Average Process Subject to Ambiguous Lévy Basis
	23.1. Introduction
	23.2. supOU process
	23.3. Optimization problems
		23.3.1. Problem description
		23.3.2. Problem D: Underestimation problem
		23.3.3. Problem U: Overestimation problem
	23.4. Application
		23.4.1. Study sites
		23.4.2. Parameter estimation
		23.4.3. Results and discussion
	23.5. Conclusion
	23.6. Acknowledgments
	23.7. References
List of Authors
Index
Other titles from ISTE in Innovation, Entrepreneurship and Management