Perna / Sibillo Mathematical and Statistical Methods for Insurance and Finance

1. Auflage 2007
ISBN: 978-88-470-0704-8
Verlag: Springer Milan
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 208 Seiten

The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.

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.

Autoren/Hrsg.

Perna, Cira

Sibillo, Marilena

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;List of Contributors;10
4;Least Squares Predictors for Threshold Models: Properties and Forecast Evaluation;14
4.1;1 Introduction;14
4.2;2 The SETARMA Predictors;15
4.3;3 Empirical Results and Analysis;21
4.4;References;22
5;Estimating Portfolio Conditional Returns Distribution Through Style Analysis Models*;23
5.1;1 Introduction;23
5.2;2 Style Analysis;24
5.3;3 Concluding Remarks;28
5.4;References;29
6;A Full Monte Carlo Approach to the Valuation of the Surrender Option Embedded in Life Insurance Contracts*;30
6.1;1 Introduction;30
6.2;2 Notation and Assumptions;31
6.3;3 The Valuation Approach;32
6.4;4 Tests of Accuracy;34
6.5;5 Summary and Conclusions;37
6.6;References;37
7;Spatial Aggregation in Scenario Tree Reduction;38
7.1;1 Introduction;38
7.2;2 Scenario Tree Reduction Using Aggregation Methods;39
7.3;3 A Spatial Aggregation Method for Scenario Tree Reduction;40
7.4;4 Concluding Remarks;45
7.5;References;45
8;Scaling Laws in Stock Markets. An Analysis of Prices and Volumes;46
8.1;1 Introduction;46
8.2;2 Self Similarity and Scaling;47
8.3;3 Empirical Application;49
8.4;4 Conclusion and Further Developments;51
8.5;References;52
9;Bounds for Concave Distortion Risk Measures for Sums of Risks*;54
9.1;1 Introduction;54
9.2;2 The Class of Distortion Risk Measures;56
9.3;3 The Class of Concave Distortion Risk Measures;58
9.4;4 Optimal Gap Between Bounds of Risk Measures;59
9.5;5 Concluding Remarks;61
9.6;References;61
10;Characterization of Convex Premium Principles;63
10.1;1 Introduction;63
10.2;2 Insurance Premium Principles;64
10.3;3 Choquet Pricing of Insurance Risks;66
10.4;4 Distortion Risk Measures;67
10.5;5 Representation of a Class of Premium Functionals;68
10.6;References;69
11;FFT, Extreme Value Theory and Simulation to Model Non- Life Insurance Claims Dependences;71
11.1;1 Introduction;71
11.2;2 An Example of EVT, FFT and Simulation Application;72
11.3;3 Conclusions;75
11.4;References;75
12;Dynamics of Financial Time Series in an Inhomogeneous Aggregation Framework;76
12.1;1 Introduction;76
12.2;2 Market Price Dynamics;77
12.3;3 Conclusions;81
12.4;References;82
13;A Liability Adequacy Test for Mathematical Provision*;84
13.1;1 Liability Adequacy Test and Contingency Reserve;84
13.2;2 A Solvency Perspective via the Quantile Reserve;86
13.3;3 A Simulative Application;87
13.4;References;89
14;Iterated Function Systems, IteratedMultifunction Systems, and Applications*;91
14.1;1 Introduction;91
14.2;2 Iterated Function Systems (IFS);92
14.3;3 Iterated Multifunction Systems;94
14.4;4 Applications;95
14.5;References;97
15;Remarks on Insured Loan Valuations;99
15.1;1 Introduction;99
15.2;2 The Insured Loan Portfolio: Cash Flow Structure and Reserve Fair Value;100
15.3;3 The Application to a Case of Equivalent Products;102
15.4;4 Conclusions;105
15.5;References;105
16;Exploring the Copula Approach for the Analysis of Financial Durations;107
16.1;1 Introduction;107
16.2;2 ACDModels;107
16.3;3 Copula Functions;109
16.4;4 DataAnalysis;110
16.5;5 Concluding Remarks;114
16.6;References;114
17;Analysis of Economic Fluctuations: A Contribution from Chaos Theory*;115
17.1;1 Introduction;115
17.2;2 Non-linear Deterministic Systems. Is Economy a Chaotic System?;116
17.3;3 Conclusion;119
17.4;References;119
18;Generalized Influence Functions and Robustness Analysis;121
18.1;1 Introduction;121
18.2;2 Prohorov Distance and Qualitative Robustness;122
18.3;3 Influence Function and B-robustness;122
18.4;4 Generalized Derivatives for Scalar and Vector Functions;125
18.5;5 Generalized Influence Functions and Generalized B-robustness;126
18.6;References;128
19;Neural Networks for Bandwidth Selection in Non- Parametric Derivative Estimation;129
19.1;1 Introduction;129
19.2;2 Local Polynomials for Non-parametric Derivative Estimation;130
19.3;3 The Selection of the Smoothing Parameter;131
19.4;4 An Experiment on Simulated Data;132
19.5;References;136
20;ComparingMortality Trends via Lee-CarterMethod in the Framework of Multidimensional Data Analysis;138
20.1;1 Introduction and Basic Notations;138
20.2;2 The Lee- Carter Model in the Framework of Multidimensional Data Analysis;139
20.3;3 An Application to Italian Mortality Rates in the Period 1950– 2000;141
20.4;References;145
21;Decision Making in FinancialMarkets ThroughMultivariate Ordering Procedure*;146
21.1;1 Introduction;146
21.2;2 The Ordering Procedure;148
21.3;3 The Problem of the Range of Variation;149
21.4;4 Application to Financial Markets;150
21.5;5 Conclusions;153
21.6;References;153
22;A Biometric Risks Analysis in Long Term Care Insurance;155
22.1;1 Introduction;155
22.2;2 Multiple State Model;155
22.3;3 Estimation of Transition Intensities;157
22.4;4 Demographic Scenarios;157
22.5;5 Benefits, Premiums, and Reserve;158
22.6;6 Risk Analysis;159
22.7;7 Portfolio Simulation Results;160
22.8;References;162
23;Clustering Financial Data for Mutual Fund Management;163
23.1;1 Introduction;163
23.2;2 Clustering Financial Data;165
23.3;3 Applications;166
23.4;4 Concluding Remarks;169
23.5;References;170
24;Modeling Ultra-High-Frequency Data: The S&P 500 Index Future;171
24.1;1 Introduction;171
24.2;2 DSPP with Generalized Shot Noise Intensity;172
24.3;3 The S&P 500 Index Future Data Set;175
24.4;References;178
25;Simulating a Generalized Gaussian Noise with Shape Parameter 1/ 2;179
25.1;1 Introduction;179
25.2;2 The Generalized Gaussian Density;180
25.3;3 Simulating the Generalized Gaussian Distribution;181
25.4;4 Simulating the Generalized Gaussian Distribution with;182
25.5;1/ 2;182
25.6;5 Conclusions;185
25.7;References;186
26;Further Remarks on Risk Profiles for Life Insurance Participating Policies;187
26.1;1 Introduction;187
26.2;2 The Quantile Reserve and the Actuarial Liabilities;188
26.3;3 The Mathematical Model;188
26.4;4 Numerical Proxies for the Quantile Reserve via Simulation Procedures;190
26.5;References;193
27;Classifying Italian Pension Funds via GARCH Distance;194
27.1;1 Introduction;194
27.2;2 Distance Between GARCH Models;196
27.3;3 A Classification of Funds;198
27.4;4 Concluding Remarks;201
27.5;References;202
28;The Analysis of Extreme Events – Some Forecasting Approaches*;203
28.1;1 Introduction;203
28.2;2 Kinds of Approaches for the Analysis of Extreme Events;205
28.3;3 Self- Organized Criticality;206
28.4;4 Differences Between SOC and TVP Literatures;207
28.5;5 Forecasting and SOC – Why Markets Crash;208
28.6;6 Conclusion;208
28.7;References;208
29;Subject Index;210
30;Author Index;212