Mathematical and Statistical Methods for Actuarial Sciences and Finance (eBook)

Marco Corazza has a PhD in "Mathematics for the Analysis of Financial Markets" and is an associate professor at the Department of Economics of the Ca' Foscari University of Venice (Italy). His main research interests include static and dynamic portfolio management theories; trading system models; machine learning applications in finance; bio-inspired optimization techniques; multi-criteria methods for economic decision support; port scheduling models and algorithms; and non-standard probability distributions in finance. He has participated in several research projects, at both the national and international level, and is the author/coauthor of one hundred and twenty scientific publications, some of which have received national and international awards. He is also editor-in-chief of the international scientific journal "Mathematical Methods in Economics and Finance", and is a member of the scientific committees of several conferences and of some private companies. His combines his academic activities with consulting services. María Durbán is a professor of Statistics at Universidad Carlos III de Madrid (Spain). Her main areas of research are non-parametric regression, smooth mixed models and regression models for spatio-temporal data. She has numerous publications in these topics and their application in areas such as epidemiology, economics, and environmental sciences. She has been part of many scientific committees of international conferences.  Aurea Grané is a professor of Statistics at Universidad Carlos III de Madrid (Spain). Her research interests are mainly in goodness-of-fit, multivariate techniques for mixed-type data, functional data analysis and she has published numerous papers on these topics in international journals. She has been a member of several scientific committees of international conferences, and was co-director of the Master in Quantitative Techniques for the Insurance Sector and vice-director of the Department of Statistics at Universidad Carlos III de Madrid.Cira Perna is a professor of Statistics and head of the Department of Economics and Statistics, University of Salerno (Italy). Her research mainly focuses on non-linear time series, artificial neural network models and resampling techniques, and she has published numerous papers on these topics in national and international journals. She has been a member of several scientific committees of national and international conferences.Marilena Sibillo is a professor of Mathematical Methods for Economics, Finance and Actuarial Sciences at the University of Salerno (Italy). She has several international editing engagements and is the author of over a hundred publications. Her research interests are mainly in longevity risk in life contracts, de-risking strategies, personal pension products and mortality forecasting.

Preface 5
Contents 6
About the Editors 13
The Effect of Rating Contingent Guidelines and Regulation Around Credit Rating News 15
1 Introduction 15
2 Rating-Based Investment Guidelines 16
3 Data and Analysis Implementation 17
4 Results 19
5 Concluding Remarks 19
References 19
Practical Problems with Tests of Cointegration Rank with Strong Persistence and Heavy-Tailed Errors 20
1 Introduction 20
2 Power of Tests in the Heteroskedastic VAR Model with Heavy-Tailed Errors 21
3 Empirical Results 23
4 Conclusions 23
References 24
Inference in a Non-Homogeneous Vasicek Type Model 25
1 Introduction and Background 25
2 The Model 26
3 Fitting the Model 27
4 A Simulation Study 27
References 28
Small Sample Analysis in Diffusion Processes: A Simulation Study 30
1 Introduction 30
2 ML Estimation and Bootstrap Correction 31
3 Simulation Experiment and Results 32
References 34
Using Deepest Dependency Paths to Enhance Life ExpectancyEstimation 35
1 Introduction 35
2 Methodology 36
3 Results 38
References 41
The Optimal Investment and Consumption for Financial Markets Generated by the Spread of Risky Assets for the Power Utility 42
1 Market Model 42
2 Stochastic Programming Method 43
3 Main Results 45
References 46
Combining Multivariate Volatility Models 47
1 Introduction 47
2 MCS Combination Strategy 48
3 Empirical Analysis 49
References 50
Automatic Detection and Imputation of Outliers in Electricity Price Time Series 52
1 Introduction 52
2 Time Series Outlier Detection and Imputation 53
3 Results and Discussion 54
References 56
Bayesian Factorization Machines for Risk Management and Robust Decision Making 57
1 Introduction 57
2 Prediction 58
3 Multiobjective Optimization 60
References 60
Improving Lee-Carter Forecasting: Methodology and Some Results 62
1 Introduction and Literature 62
2 Mathematical Framework and Empirical Methodology 63
3 Graphical Assessment of the Predictive Accuracy of the ``mLC'' Model 64
4 Concluding Remarks 65
References 66
The Bank Tailored Integrated Rating 67
1 Motivation and Methodology 67
2 Stylized Mathematical Approach 68
3 Summaries and Future Developments 69
Appendix 70
References 71
A Single Factor Model for Constructing Dynamic Life Tables 72
1 Single Factor Model 72
1.1 Adjusting a Sensitivity Function to bx,x* 73
1.2 Forecasting Mortality Rates 74
2 Lee-Carter (1992) Model 74
3 Comparison Between the Single Factor Model and the Lee-Carter Model 75
References 76
Variable Annuities with State-Dependent Fees 77
1 Introduction 77
2 The Structure of the Contract 78
3 Valuation Framework 79
3.1 The Static Approach 79
3.2 The Mixed Approach 80
4 Numerical Implementation 80
References 82
Dynamic Policyholder Behavior and Surrender Option Evaluation for Life Insurance 83
1 Introduction 83
2 A Model for the Lapse Rate Estimation According to Policyholder Behavior 84
2.1 Step 1 85
2.2 Step 2 85
3 Some Numerical Results 86
References 87
Classification Ratemaking via Quantile Regression and a Comparison with Generalized Linear Models 88
1 Introduction 88
2 A Quantile Premium Principle Based on a Two-Part Model 89
2.1 The Two Part Model for the Individual Risk Model 89
2.2 A Quantile Premium Principle Based on a Two-Part Model 90
3 Simulation Study 91
References 92
An Empirical Analysis of the Lead Lag Relationship Between CDS and Stock Market 93
1 Introduction 93
2 Data and Methodology 94
3 Results 94
4 Conclusions 96
References 96
Integration of Non-financial Criteria in Equity Investment 97
1 Introduction 97
2 Including Non-financial Criteria 98
3 Constrained Tracking Error Approach 99
4 Conclusion 100
References 100
A Generalized Moving Average Convergence/Divergence for Testing Semi-strong Market Efficiency 101
1 Introduction 101
2 The Proposed Indicator 102
3 Nonparametric Bootstrap Test 103
3.1 Simulations 104
4 Empirical Test Results 104
References 105
Periodic Autoregressive Models with Multiple Structural Changes by Genetic Algorithms 106
1 Model Description and Estimation 106
2 Application and Conclusions 108
References 109
Mortality Projection Using Bayesian Model Averaging 110
1 Introduction 110
2 The Bayesian Model Averaging (BMA) 111
3 Mortality Projection Applying BMA 111
4 Final Remarks 113
References 113
Robust Time-Varying Undirected Graphs 115
1 Introduction 115
2 Methodology 116
3 Algorithm 117
4 Simulation Study 118
References 118
Two-Sided Skew and Shape Dynamic Conditional Score Models 119
1 Introduction 119
2 Two-Sided Skew and Shape Distribution 120
3 2SSS Dynamic Conditional Score Model 121
References 122
Sparse Networks Through Regularised Regressions 123
1 Introduction 123
2 The Model 124
2.1 Spike-and-Slab EM 124
3 Application to Network Analysis 126
References 126
Approximate EM Algorithm for Sparse Estimation of Multivariate Location–Scale Mixture of Normals 127
1 Introduction 127
2 Multivariate Model Specifications 128
3 Parameters Estimation via FFT–EM Algorithm 129
4 Portfolio Application 130
References 130
An Extension of Multidimensional Scaling to Several Distance Matrices, and Its Application to the Italian Banking Sector 131
1 Introduction 131
2 Method 132
3 Analysis 133
References 134
Disagreement in Signed Financial Networks 136
1 Introduction 136
2 Disagreement in Unsigned Directed Network 137
3 The Lifted Dynamics and Disagreement in Signed Networks 138
References 139
Bayesian Tensor Binary Regression 140
1 Bayesian Markov Switching Binary Tensor Regression Model 140
2 Bayesian Inference 141
3 Simulation and Application 142
4 Conclusions 144
References 144
Bayesian Tensor Regression Models 145
1 Bayesian Tensor Regression Model 145
2 Bayesian Inference 146
3 Simulation and Application 147
4 Conclusions 149
References 149
Bayesian Nonparametric Sparse Vector Autoregressive Models 150
1 Introduction 150
2 The Vector Autoregressive model 151
3 Bayesian Nonparametric Sparse VAR 152
4 Simulation Results 153
5 Conclusions 155
References 155
Logistic Classification for New Policyholders Taking into Account Prediction Error 156
1 Introduction 156
2 Mean Squared Error for New Observations 157
3 Application: Credit Scoring 158
References 160
Conditional Quantile-Located VaR 161
1 Methods 161
2 Empirical Results 163
References 165
Probability of Default Modeling: A Machine Learning Approach 166
1 Introduction 166
2 Methodology 167
2.1 Data Used 168
2.2 Main Results 168
3 Conclusion 169
References 169
Risk/Return Analysis on Credit Exposure: Do Small Banks Really Apply a Pricing Risk-Based on Their Loans? 171
1 Introduction 171
2 Methodology 172
2.1 Data Used 172
2.2 Results 173
3 Conclusion 173
References 176
Life Insurers' Asset-Liability Dependency and Low-Interest Rate Environment 177
1 Introduction 178
2 Data and Methodology 178
3 Empirical Results 179
4 Conclusions 180
References 181
Modelling the Australian Electricity Spot Prices: A VAR-BEKK Approach 182
1 Introduction and Motivation 182
2 Methods and Results 183
References 188
Cyber Risk Management: A New Challenge for ActuarialMathematics 189
1 Introduction 189
2 Peculiarities of Cyber Insurance 190
2.1 Some Recent Results in Economic and Actuarial Literature 191
3 Information Technology for Cyber Insurance 191
References 192
Predicting the Volatility of Cryptocurrency Time-Series 193
1 The Volatility of Cryptocurrencies 193
2 Forecast Analysis and Model Comparison 195
3 Conclusion 196
References 196
A Generalized Error Distribution-Based Method for Conditional Value-at-Risk Evaluation 198
1 Introduction 198
2 The Generalized Error Distribution and the G.E.D. Copula 199
3 The Methodology 200
4 Conclusions 201
References 201
Risk-Return Optimization for Life Insurance Portfolios 202
1 Introduction: The Life Insurance Matching Strategy and Movements of the Term Structure 203
2 Passive Strategy: Minimizing the “Immunization Risk” 203
3 Active Strategy: The Risk-Return Tradeoff Optimization 204
4 Conclusions and Further Developments 206
References 207
When Is Utilitarian Welfare Higher Under Insurance Risk Pooling? 208
1 Outline of Our Approach 208
2 Model Set-Up 209
2.1 Insurance Demand from the Individual Viewpoint 209
2.2 Insurance Demand from the Insurer's Viewpoint 210
2.3 Market Equilibrium and Social Welfare 210
3 Results for Iso-Elastic Demand 211
4 Discussion 212
References 212
The Value of Information for Optimal Portfolio Management 213
1 Introduction 213
2 The Model 214
3 The Full Information Case 215
4 The Partial Information Case 216
5 Conclusion 216
References 217
Risk and Uncertainty for Flexible Retirement Schemes 218
1 Motivation 219
2 The Italian Mortality Experience 219
3 Dealing with Model Uncertainty 219
4 A Flexible Retirement Scheme 220
5 Conclusion and Further Developments 221
References 222
Comparing Possibilistic Portfolios to Probabilistic Ones 223
1 Introduction 223
2 The Theoretical Comparison 225
3 The Empirical Comparison 226
References 227
Some Critical Insights on the Unbiased Efficient Frontier à la Bodnar& Bodnar
1 Introduction 228
2 Unbiased Estimator of the Efficient Frontier 229
3 Our Main Results 230
3.1 The Asymptotic Behavior of the Biased Estimator 230
3.2 The ``Strange'' Behavior of the Unbiased Estimator 230
3.3 The Operational Effectiveness of the Unbiased Estimator 231
References 232
Numerical Solution of the Regularized Portfolio Selection Problem 233
1 Introduction 233
2 Regularized Portfolio Selection Model 234
3 Bregman Iteration for Portfolio Selection 235
References 236
Forecasting the Equity Risk Premium in the European MonetaryUnion 237
1 Introduction 237
2 In-Sample Analysis 238
3 Out-of-Sample Analysis 239
4 Asset Allocation 239
5 Summary of Most Important Results 239
References 241
Statistical Learning Algorithms to Forecast the Equity Risk Premium in the European Union 242
1 Introduction 242
2 Methodology 243
2.1 CART Models 243
2.2 Ensemble Models 244
3 The Model 244
3.1 The Data 244
3.2 Out-of-Sample Predictions 246
4 Results 246
References 248
Evaluating Variable Annuities with GMWB When Exogenous Factors Influence the Policy-Holder Withdrawals 249
1 The Framework 249
2 The Evaluation Model 250
3 Numerical Results 251
Reference 253
A Continuous Time Model for Bitcoin Price Dynamics 254
1 Introduction 254
2 The Model 255
3 Risk Neutral Measure and Option Pricing 255
4 A Numerical Example 257
References 258
Forecasting the Volatility of Electricity Prices by Robust Estimation: An Application to the Italian Market 259
1 Introduction 260
2 A Robust SETAR Model for Electricity Prices 260
3 Robust Volatility Estimation Through the Forward Search 261
References 263
``Money Purchase'' Pensions: Contract Proposals and Risk Analysis 264
1 Personal Pension Products 264
2 Variable Annuities with Participating Benefits: Notations and Recalls 265
3 The Demographic Risk Filters 266
References 267
What If Two Different Interest Rates Datasets Allow for Describing the Same Financial Product? 268
1 Introduction 269
2 Discrepancies in the Datasets: Impact on the Volatility Term Structure and on the Interest Rate Projections 269
3 Pricing Derivatives: Two Applicative Cases 270
References 272
An Integrated Approach to Explore the Complexity of Interest Rates Network Structure 273
1 Introduction 273
2 Mathematical Background 274
2.1 Quantile Regression 274
3 A Practical Application 275
4 Conclusion 276
References 277
Estimating Regulatory Capital Requirements for Reverse Mortgages: An International Comparison 278
1 Paper Summary 278
References 281
A Basic Social Pension for Everyone? 282
1 Introduction 282
2 One Basic Social Pension and One Funding Model 283
3 Application 284
4 Conclusions 285
References 286
A Copula-Based Quantile Model 287
1 Introduction 287
2 Modelling and Data 288
3 Conclusions 290
References 291
International Longevity Risk Pooling 292
1 Motivation and Related Literature 292
2 Pooling Metrics and Impact 293
3 Conclusions 295
References 296
A Two-Steps Mixed Pension System: An Aggregate Analysis 297
1 Introduction 298
2 The Two-Steps Mixed System 298
3 Aggregate Perspective 300
4 Concluding Comments on Transition Possibilities 300
References 302
The Influence of Dynamic Risk Aversion in the Optimal PortfolioContext 303
1 Introduction 303
2 Main Results and Findings: The Certainty-Equivalent 305
References 306
Socially Responsible Investment, Should You Bother? 308
1 Introduction 308
2 Relationship Between Socially Responsible Performance and Financial Performance 309
3 Portfolios Composition and Data Sample 310
4 Empirical Analysis 310
5 Conclusion 311
References 312
Measuring Financial Risk Co-movement in Commodity Markets 313
1 Introduction 313
2 Methodology 314
2.1 Selecting a Downside Risk Measure 314
2.2 Constructing Financial Downside Risk Maps with MDS 315
3 Main Results 315
4 Conclusions 316
References 316
Helping Long Term Care Coverage via Differential on Mortality? 317
1 Long Term Care as a Coverage 317
2 Differential on Mortality 318
3 An Application to Spain 319
4 Conclusions 321
References 321
Tuning a Deep Learning Network for Solvency II: Preliminary Results 322
1 Introduction 322
2 Numerical Set-Up 324
3 Results 324
References 325
Exploratory Projection Pursuit for Multivariate Financial Data 327
1 Introduction 327
2 Results 328
References 330
The Rearrangement Algorithm of Puccetti and Rüschendorf: Proving the Convergence 332
1 Introduction 332
2 The Rearrangement Algorithm 333
3 Proof of Convergence 335
References 336
Automatic Balancing Mechanisms in Practice: What Lessons for Pension Policy Makers? 337
1 Introduction 338
2 The US Social Security Fiscal Cliff: Automatic and Rough Adjustment Through Pension Benefits 338
3 The Swedish NDC Experiment: Reinforcing Automatic Adjustment Mechanisms by Introducing an Explicit ABM 339
4 Canada's Second Pillar: An Automatic Adjustment Through Contribution Scattered by the Absence of Political Choice 340
References 341
Empirical Evidence from the Three-Way LC Model 342
1 Introduction 342
2 The Three-Way Lee-Carter Model 343
3 The Analysis and Interpretation of the 3-Way LC Model 344
4 The Advantage of Introducing a Third Way in the Analysis 344
5 The Factorial Representations 345
References 346
Variable Selection in Estimating Bank Default 347
1 Introduction 347
2 Statistical Model 348
3 Screening for High Dimensional GEV Models 349
References 350
Multiple Testing for Different Structures of Spatial Dynamic Panel Data Models 352
1 The SDPD Models 352
2 A Strategy for Testing the Particular Structure of SDPD Models 353
3 Bootstrap Scheme for the Multiple Testing Procedure 354
References 355
Loss Data Analysis with Maximum Entropy 356
1 Introduction 357
2 The Standard Method of Maximum Entropy (SME) 357
3 Examples 358
3.1 Notes and Comments 358
Reference 360
Real-World Versus Risk-Neutral Measures in the Estimation of an Interest Rate Model with Stochastic Volatility 361
1 Introduction 361
2 The Valuation Model 362
3 Results and Approximations 363
4 Empirical Application 364
References 364
Extensions of Fama and French Models 366
1 Introduction and Methodology 366
1.1 Aim 366
1.2 Methodology 366
2 Main Results and Concluding Remarks 367
References 368
The Islamic Financial Industry: Performance of Islamic vs. Conventional Sector Portfolios 369
1 Introduction 369
2 Performance 370
3 Main Results and Concluding Remarks 371
References 373
Do Google Trends Help to Forecast Sovereign Risk in Europe? 374
1 Introduction 374
2 Background Literature 375
3 Data 375
4 Results 376
5 Conclusions 377
References 377
The Contribution of Usage-Based Data Analytics to Benchmark Semi-autonomous Vehicle Insurance 379
1 Introduction 379
2 Data and Methods 380
3 Speed Reduction and Safety 381
4 Conclusions 382
References 382
Some Empirical Evidence on the Need of More Advanced Approaches in Mortality Modeling 384
1 Mortality Models Based on Legendre Polynomials 384
2 Empirical Investigation 386
References 389
Could Machine Learning Predict the Conversion in Motor Business? 390
1 Introduction 390
2 Description of the Data Set 391
3 Machine Learning Models 391
3.1 Generalized Linear Model (GLM) 391
3.2 Classification and Regression Tree (CART) 391
3.3 Random Forest (RF) 392
3.4 Gradient Boosted Tree (BOOST) 392
4 Models Calibration 392
5 Analysis of Results 393
References 394
European Insurers: Interest Rate Risk Management 395
1 Introduction and Methodology 395
1.1 Aim 395
1.2 Data and Methodology 396
2 Main Results and Concluding Remarks 398
References 398
Estimation and Prediction for the Modulated Power Law Process 400
1 Introduction 400
2 Estimation of the MPLP Parameters 401
3 Prediction of the Next Failure Time 403
4 Application to Some Real Data Set 403
References 404
The Level of Mortality in Insured Populations 405
1 Introduction 406
2 Mortality: Current and Future. Solvency II and IFRS 17 406
3 Methodology and Data 407
4 Results and Conclusions 408
References 409
Kurtosis Maximization for Outlier Detection in GARCH Models 411
1 Introduction 411
2 Main Result 412
References 414
Google Searches for Portfolio Management: A Risk and ReturnAnalysis 416
1 Introduction 416
2 Google Trends 417
3 Asset Allocation Based on Google Search Volumes 418
References 420
The Challenges of Wealth and Its Intergenerational Transmission in an Aging Society 421
1 Introduction 421
2 A Present Wealth Situation Which Is Both Massive and Noxious 422
3 `Patrimonialization' Due to Rising Longevity and Other Changes 423
4 Possible Tax or Social Remedies: The Taxfinh Program 424
References 425
Bivariate Functional Archetypoid Analysis: An Application to Financial Time Series 426
1 Introduction 426
2 Data 427
3 Methodology 427
3.1 AA and ADA for (Standard) Multivariate Data 427
3.2 AA and ADA for Functional Data 428
4 Results 428
5 Conclusions 429
References 429
A Note on the Shape of the Probability Weighting Function 430
1 Introduction 430
2 An Application to Premium Calculation 432
References 433
Disability Pensions in Spain: A Factor to Compensate Lifetime Losses 435
1 Pension Systems: The Case of Spain 435
2 The Main Component of Spanish Pensions: Public Non-means-tested Benefit 436
3 Underlying Differences Between the Beneficiaries of a Regular Pension and the Beneficiaries of a Disability Pension 437
4 A Simple Actualisation Factor to Compensate Differences Between the Beneficiaries of a Regular Pension and the Beneficiaries of a Disability Pension 438
References 439
A Minimum Pension for Older People via Expenses Rate 440
1 Introduction 440
2 Long Term Care Problem: Consume Paths 441
3 An Application to Spain 442
4 Conclusion 443
References 443
A Comparative Analysis of Neuro Fuzzy Inference Systems for Mortality Prediction 445
1 Introduction 445
2 Adaptive Neuro Fuzzy Systems 446
3 The Lee Carter Model 446
4 Application to Mortality Dataset 447
5 Conclusions 448
References 448
Financial Networks and Mechanisms of Business Capture in Southern Italy over the First Global Wave (1812–1913): A Network Analysis Approach 450
1 Introduction 450
2 The South of Italy in the 1st Global Wave: Context and Data 451
3 The Evolution of the Role of the Economic Actors in Naples: A Network Approach 452
4 A First Discussion 453
References 454
Modeling High-Frequency Price Data with Bounded-Delay Hawkes Processes 455
1 Introduction 455
2 Beta Delay Hawkes Model 456
3 Experiments 457
4 Conclusion 459
References 459
Pricing Illiquid Assets by Entropy Maximization Through Linear Goal Programming 460
1 Introduction 461
2 Notations and Preliminaries 461
3 The Goal Programming Method 462
4 Conclusions 464
References 464