Proceedings of the Forum "Math-for-Industry" 2018: Big Data Analysis, AI, Fintech, Math in Finances and Economics (Mathematics for Industry, 35)

This volume includes selected technical papers presented at the Forum “Math-for-Industry” 2018. The papers written by eminent researchers and academics working in the area of industrial mathematics from the viewpoint of financial mathematics, machine learning, neural networks, inverse problems, stochastic modelling, etc., discuss how the ingenuity of science, technology, engineering and mathematics are and will be expected to be utilized. This volume focuses on the role that mathematics-for-industry can play in interdisciplinary research to develop new methods. The contents are useful for researchers both in academia and industry working in interdisciplinary sectors. Organization Preface Contents About the Editors Copula-Based Estimation of Value at Risk for the Portfolio Problem 1 Introduction 2 Preliminary 2.1 Value at Risk 2.2 Copula 3 Determination Formula 4 Empirical Study 4.1 Margins Modelling 4.2 Copula-Based Approach 4.3 Backtesting 5 Discussions References Notes on Backward Stochastic Differential Equations for Computing XVA 1 Introduction 2 BSDE with a Random Horizon in a Progressively Enlarged Filtration 2.1 Setup 2.2 Existence, Uniqueness, and Construction of Solution 2.3 Markovian Model 3 XVA Calculation via BSDE 3.1 Non-defaultable/Defaultable Risky Assets 3.2 Defaultable Derivative Security 3.3 Dynamic Portfolio Strategy 3.4 Deriving BSDE 3.5 Hedging Problem 3.6 Markovian Model 4 Results 4.1 Results on Arbitrage 4.2 Results on XVA 4.3 Perturbed BSDEs References An Overview of Exact Solution Methods for Guaranteed Minimum Death Benefit Options in Variable Annuities 1 Introduction 2 The Direct Integration Method 3 The Partial Differential Equation Method 4 The Discounted Density Method 5 Extensions of the Analytic Methods to Related Problems 6 Conclusions and Future Research Directions References Mathematical Modeling and Inverse Problem Approaches for Functional Clothing Design Based on Thermal Mechanism 1 Background of the IPTMD 2 Mathematical Model of Dynamic Heat–Moisture Transfer within the TCC System 3 Mathematical Model of Dynamic Heat Transfer within the TPC System 3.1 Fractional Description for Superdiffusion 3.2 Mathematical Model for TPC System 4 Numerical Computation for the TPC Direct Problems to Determine the Fractional Order 4.1 Numerical Algorithm 4.2 Parameters and Conditions in Numerical Process 4.3 Numerical Result 5 Mathematical Formulation for Inverse Problems for the TCC/TPC Design 5.1 Mathematical Reformulation of the TCC Inverse Problems (IP 1) 5.2 Mathematical Reformulation of the TPC Inverse Problems (IP 2) 6 Computational Strategy for the IPTMD of the TCC/TPC Design 6.1 Deterministic Case: Least Squares Method and Regularization Method 6.2 Stochastic Case: Bayesian Inference Method and Maximum Probability Method 6.3 Computational Examples for IPTMD 7 Concluding Remarks and Future Studies References Determinantal Reinforcement Learning with Techniques to Avoid Poor Local Optima 1 Introduction 2 Determinantal SARSA 3 Avoiding Poor Local Optima 4 Experiments 5 Conclusion References Surface Denoising Based on Normal Filtering in a Robust Statistics Framework 1 Introduction 1.1 Notation 1.2 Related Work 1.3 Face Normal Filtering Versus Vertex Position Filtering 1.4 Scope 2 Robust Statistical Estimation 2.1 M-estimators 3 Face Normal Filtering in the Robust Statistics Framework 3.1 Unilateral Normal Filtering 3.2 Bilateral Normal Filtering 4 Point Set Surface Denoising in the Robust Statistics Framework 4.1 Unilateral Normal Filtering 4.2 Bilateral Normal Filtering 5 Experiments and Results 6 Conclusion References Unique Continuation on a Sphere for Helmholtz Equation and Its Numerical Treatments 1 Introduction 2 Main Results 3 Numerical Method and Examples 4 Conclusion References Huberization Image Restoration Model from Incomplete Multiplicative Noisy Data 1 Introduction 2 The Algorithm for the Double Regularizing Image Restoration Model 3 Numerical Experiments 4 Conclusion References A Brief Review of Some Swarming Models Using Stochastic Differential Equations 1 Introduction 2 Model Equations 2.1 General Model 2.2 Model in Free Space 2.3 Avoiding Obstacle Model 2.4 Foraging Model 3 Numerical Study on Swarming Models 3.1 Swarm Cohesiveness 3.2 Obstacle Avoiding Behavioral Patterns 3.3 Foraging Advantage 4 Conclusion References