Mathematical and Statistical Methods for Insurance and Finance (eBook)

Cira Perna has received the Degree in Mathematics from the University of Naples in 1983 and the M. Phil. in Statistics from the CSREAM, University of Naples, in 1985. She had Faculty positions, as Associate Professor, at the University of Calabria (1992-1994) and at the University of Salerno (1994-1999). She has been Professor of Statistics at the University of Salerno since 2000. She has published over 50 technical papers in journals and books. Her current research focuses on non linear time series analysis, artificial neural network models, resampling techniques. She is a member of the Italian Statistical Society and of the IASC. She is also in the board of the ANSET (Italian Time Series Analysis Research Group). Marilena Sibillo: After graduating in Quantitative Economics at the University of Naples Federico II, she worked at the University of Naples Federico II as a Researcher and taught at the Universities of Sassari and Salerno as Associate Professor. Since 2004 she is Professor in Financial Mathematics. She is author of several papers, mostly in Actuarial Mathematics, published in international specialized journal. At present her research is focused on the risk analysis in actuarial portfolio valuations.

Preface 5
Contents 7
List of Contributors 10
Least Squares Predictors for Threshold Models: Properties and Forecast Evaluation 14
1 Introduction 14
2 The SETARMA Predictors 15
3 Empirical Results and Analysis 21
References 22
Estimating Portfolio Conditional Returns Distribution Through Style Analysis Models* 23
1 Introduction 23
2 Style Analysis 24
3 Concluding Remarks 28
References 29
A Full Monte Carlo Approach to the Valuation of the Surrender Option Embedded in Life Insurance Contracts* 30
1 Introduction 30
2 Notation and Assumptions 31
3 The Valuation Approach 32
4 Tests of Accuracy 34
5 Summary and Conclusions 37
References 37
Spatial Aggregation in Scenario Tree Reduction 38
1 Introduction 38
2 Scenario Tree Reduction Using Aggregation Methods 39
3 A Spatial Aggregation Method for Scenario Tree Reduction 40
4 Concluding Remarks 45
References 45
Scaling Laws in Stock Markets. An Analysis of Prices and Volumes 46
1 Introduction 46
2 Self Similarity and Scaling 47
3 Empirical Application 49
4 Conclusion and Further Developments 51
References 52
Bounds for Concave Distortion Risk Measures for Sums of Risks* 54
1 Introduction 54
2 The Class of Distortion Risk Measures 56
3 The Class of Concave Distortion Risk Measures 58
4 Optimal Gap Between Bounds of Risk Measures 59
5 Concluding Remarks 61
References 61
Characterization of Convex Premium Principles 63
1 Introduction 63
2 Insurance Premium Principles 64
3 Choquet Pricing of Insurance Risks 66
4 Distortion Risk Measures 67
5 Representation of a Class of Premium Functionals 68
References 69
FFT, Extreme Value Theory and Simulation to Model Non- Life Insurance Claims Dependences 71
1 Introduction 71
2 An Example of EVT, FFT and Simulation Application 72
3 Conclusions 75
References 75
Dynamics of Financial Time Series in an Inhomogeneous Aggregation Framework 76
1 Introduction 76
2 Market Price Dynamics 77
3 Conclusions 81
References 82
A Liability Adequacy Test for Mathematical Provision* 84
1 Liability Adequacy Test and Contingency Reserve 84
2 A Solvency Perspective via the Quantile Reserve 86
3 A Simulative Application 87
References 89
Iterated Function Systems, IteratedMultifunction Systems, and Applications* 91
1 Introduction 91
2 Iterated Function Systems (IFS) 92
3 Iterated Multifunction Systems 94
4 Applications 95
References 97
Remarks on Insured Loan Valuations 99
1 Introduction 99
2 The Insured Loan Portfolio: Cash Flow Structure and Reserve Fair Value 100
3 The Application to a Case of Equivalent Products 102
4 Conclusions 105
References 105
Exploring the Copula Approach for the Analysis of Financial Durations 107
1 Introduction 107
2 ACDModels 107
3 Copula Functions 109
4 DataAnalysis 110
5 Concluding Remarks 114
References 114
Analysis of Economic Fluctuations: A Contribution from Chaos Theory* 115
1 Introduction 115
2 Non-linear Deterministic Systems. Is Economy a Chaotic System? 116
3 Conclusion 119
References 119
Generalized Influence Functions and Robustness Analysis 121
1 Introduction 121
2 Prohorov Distance and Qualitative Robustness 122
3 Influence Function and B-robustness 122
4 Generalized Derivatives for Scalar and Vector Functions 125
5 Generalized Influence Functions and Generalized B-robustness 126
References 128
Neural Networks for Bandwidth Selection in Non- Parametric Derivative Estimation 129
1 Introduction 129
2 Local Polynomials for Non-parametric Derivative Estimation 130
3 The Selection of the Smoothing Parameter 131
4 An Experiment on Simulated Data 132
References 136
ComparingMortality Trends via Lee-CarterMethod in the Framework of Multidimensional Data Analysis 138
1 Introduction and Basic Notations 138
2 The Lee- Carter Model in the Framework of Multidimensional Data Analysis 139
3 An Application to Italian Mortality Rates in the Period 1950– 2000 141
References 145
Decision Making in FinancialMarkets ThroughMultivariate Ordering Procedure* 146
1 Introduction 146
2 The Ordering Procedure 148
3 The Problem of the Range of Variation 149
4 Application to Financial Markets 150
5 Conclusions 153
References 153
A Biometric Risks Analysis in Long Term Care Insurance 155
1 Introduction 155
2 Multiple State Model 155
3 Estimation of Transition Intensities 157
4 Demographic Scenarios 157
5 Benefits, Premiums, and Reserve 158
6 Risk Analysis 159
7 Portfolio Simulation Results 160
References 162
Clustering Financial Data for Mutual Fund Management 163
1 Introduction 163
2 Clustering Financial Data 165
3 Applications 166
4 Concluding Remarks 169
References 170
Modeling Ultra-High-Frequency Data: The S& P 500 Index Future
1 Introduction 171
2 DSPP with Generalized Shot Noise Intensity 172
3 The S& P 500 Index Future Data Set
References 178
Simulating a Generalized Gaussian Noise with Shape Parameter 1/ 2 179
1 Introduction 179
2 The Generalized Gaussian Density 180
3 Simulating the Generalized Gaussian Distribution 181
4 Simulating the Generalized Gaussian Distribution with 182
1/ 2 182
5 Conclusions 185
References 186
Further Remarks on Risk Profiles for Life Insurance Participating Policies 187
1 Introduction 187
2 The Quantile Reserve and the Actuarial Liabilities 188
3 The Mathematical Model 188
4 Numerical Proxies for the Quantile Reserve via Simulation Procedures 190
References 193
Classifying Italian Pension Funds via GARCH Distance 194
1 Introduction 194
2 Distance Between GARCH Models 196
3 A Classification of Funds 198
4 Concluding Remarks 201
References 202
The Analysis of Extreme Events – Some Forecasting Approaches* 203
1 Introduction 203
2 Kinds of Approaches for the Analysis of Extreme Events 205
3 Self- Organized Criticality 206
4 Differences Between SOC and TVP Literatures 207
5 Forecasting and SOC – Why Markets Crash 208
6 Conclusion 208
References 208
Subject Index 210
Author Index 212