Risk Management in Finance and Logistics (eBook)

Dr. Chunhui Xu is a professor in Finance and Management Science, Chiba Institute of Technology, Japan. He completed his Doctoral degree in Engineering at Tokyo Institute of Technology, and PhD in systems Engineering at Huazhong University of Science and Technology, China. His research addresses decision under uncertainty and conflicting interests, especially in financial area. Other interests include game theories, optimization techniques, and incentives design in organizations. He has served as Editor-in-Chief of Asian Journal of Management Science and Applications.  He is a senior member of IEEE and a member of INFORMS. Dr. Takayuki Shiina is a professor at Department of Industrial and Management Systems Science, School of Creative Science and Engineering, Waseda University, Japan. He received his B.E., M.E., and Doctor of Engineering from Waseda University. He has been working in the field of mathematical programming at Central Research Institute of Electric Power Industry (Japan), Northwestern University (USA), Chiba Institute of Technology (Japan). His main areas of interest are stochastic programming and integer programming. He was awarded the best paper prize with Professor John R. Birge (University of Chicago) from Japan Society of Industrial and Applied Mathematics.

Preface 7
Contents 10
Part I Risk Management in Finance 13
1 Financial Investment, Financial Risk and Risk Management 15
1.1 Financial Markets and Financial Investment 15
1.2 Main Risks in Financial Markets 17
1.3 Risk Countermeasures: Hedging and Diversifying 18
1.4 Risk Management by Diversification 19
1.5 Outline of Part I 21
2 Market Risk Measures in Financial Investments 24
2.1 Market Risk and Its Measurement 25
2.2 Variance: Fluctuation Is Taken as Risk 25
2.2.1 Definition of Variance 25
2.2.2 Estimation of Variance 26
2.3 Value at Risk: A Likely Loss Is Taken as Risk 28
2.3.1 Definition of Value at Risk 28
2.3.2 Estimation of VaR: Three Methods 29
2.3.2.1 Variance-Covariance Method 30
2.3.2.2 Historical Simulation Method 33
2.3.2.3 Monte Carlo Simulation Method 35
2.4 Conditional VaR: Expected Loss Behind VaR Is Taken as Risk 38
2.4.1 Definition of Conditional VaR 38
2.4.2 Estimation of CVaR 38
2.5 Other Risk Measures: Failure Is Taken as Risk 42
2.6 Summary 45
3 Market Risk Control in Investment Decisions 46
3.1 Portfolio Selection and Its Models 47
3.2 MV Model and Its Variations 48
3.2.1 The Base MV Model and Its Two Variations 48
3.2.2 Solving Methods for MV Based Models 49
3.2.3 Two MV Based Models with Computational Advantages 50
3.3 M-VaR Model and Its Solving Method 53
3.3.1 Methods for Solving M-VaR Models 54
3.3.1.1 Minimize VaR Approximately 54
3.3.1.2 Minimize VaR Indirectly 55
3.3.1.3 Minimize VaR Using Heuristics 55
3.3.2 Solving M-VaR Model Using the Soft Optimization Approach 56
3.3.2.1 The Ideas of the Soft Optimization Approach 56
3.3.2.2 The Algorithm for Solving Model (3.20) 57
3.4 M-CVaR Model and Its Solving Method 64
3.5 Other M-Risk Models and Solving Methods 66
3.6 Summary 68
4 Market Risk Measures for Flexible Investments 69
4.1 Flexible Investments 70
4.2 Risk Measures for Investments with Uncertain Exit Time 70
4.2.1 Period Value at Risk 71
4.2.2 Risk Measures Based on Average Loss in Time Axis 72
4.3 Estimation of PVaR with Scenario Simulation 74
4.3.1 Monte Carlo Simulation Method for Estimating PVaR 75
4.3.2 Historical Simulation Method for Estimating PVaR 77
4.4 Estimation of Risk Measures Based on Average Loss 79
4.4.1 Estimation of Risk Measures Under Complete Information About the Probabilities of Exit Time 79
4.4.2 Estimation of Risk Measures Under Partial Information About the Probabilities of Exit Time 85
4.5 Summary 88
5 Market Risk Control in Flexible Investment Decisions 89
5.1 Evaluation of Investments with Flexible Investment Term 90
5.2 Two Kinds of Model for Flexible Investment Decisions 91
5.3 M-PVaR Model and Solving Methods 92
5.3.1 Solving PVaR Minimization Model by Solving a Mixed Integer Linear Programming 92
5.3.2 Solving PVaR Minimization Model Using the Soft Optimization Approach 98
5.4 M-Risk Models and Solving Methods 99
5.4.1 M-Risk Models with Complete Probability Information Regarding Exit Time 100
5.4.2 M-Risk Models with Partial Probability Information Regarding Exit Time 101
5.5 M-Risk(t) Models and Their Solving Methods 103
5.6 Summary 110
References 111
Part II Risk Management in Logistics 114
6 Basic Results on Stochastic Programming 115
6.1 Stochastic Programming with Recourse 116
6.2 Multi-stage Stochastic Programming Model 118
6.3 Stochastic Integer Programming 123
6.4 Chance-Constrained Programming 133
6.5 Two-Stage Model Taking Variance into Account 138
7 Inventory Distribution Problem 145
7.1 Introduction 146
7.2 Lateral Transshipments 147
7.3 Numerical Experiments 152
7.4 Summary 157
8 Reorganization of Logistics Network 158
8.1 Background 159
8.2 Formulation 161
8.2.1 Sets 161
8.2.2 Parameters 161
8.2.3 Variables 161
8.3 Solution Algorithm 163
8.4 CVaR Optimization Model 168
8.5 Numerical Experiments 169
8.5.1 Node 169
8.5.2 Costs 169
8.5.3 Customer Demand 170
8.6 Conclusions 175
References 176
Appendix A Notations in Part I 179
Appendix B Historical Prices and Monthly Profit Rates of IBM and INTC: Data Used in Chap.2 180
Appendix C Historical Prices of 10 Components of the DJIA: Data Used in Chap.5 185
Index 187