Tychastic Measure of Viability Risk (eBook)

Foreword 6
Preface 10
Contents 13
Part IDescription, Illustrationand Comments of the Results 16
1 The Viabilist Portfolio Performance and Insurance Approach 17
1.1 The VPPI Robot-Insurer 17
1.1.1 The Inputs of the Asset-Liabilities Insurance Problem 18
1.1.2 Outputs of Asset-Liability Insurance Problem 20
1.2 The VPPI Risk Eradication Measure 21
1.2.1 The Hedging Exit Time Function 21
1.2.2 The Mobile Horizon MGI 22
1.3 Running the VPPI Management Rule 24
1.3.1 Insured Shares of the Portfolio 24
1.3.2 Performance Measures 26
1.3.3 The VPPI Ratchet Mechanism 28
1.3.4 The Diversification Paradox 32
1.3.5 Mathematical Formulation of the VPPI Rule 33
1.4 The VPPImpulse Management Robot-Forecaster 34
1.5 The VPPI Management Software 36
1.5.1 The Flow Chart of the VPPI Algorithm 37
1.5.2 The Flow Chart of the VPPImpulse Software 38
2 Technical and Quantitative Analysis of Tubes 40
2.1 Tychastic Gauge and Derivatives of the Price Tubes 41
2.2 Forecasting the Price Tube 43
2.3 Sensitivity to the Tychastic Gauge 51
2.4 Trend Reversal: From Bear to Bull and Back 53
2.4.1 Trendometer 53
2.4.2 Trend Jerkiness and Eccentricities 54
2.4.3 Detecting Extrema and Measuring Their Jerkiness 58
2.4.4 Differential Connection Tensor of a Family of Series 61
2.5 Dimensional Rank Analysis 70
2.6 Detecting Patterns of Evolutions 72
2.7 Classification of Indicators Used in Technical Analysis 74
3 Uncertainty on Uncertainties 76
3.1 Heterodox Approaches 77
3.1.1 A priori Defined Management Rules 77
3.1.2 The Uncertain Hand 79
3.1.3 Quantitative and Qualitative Insurance Evaluations and Measures 80
3.2 Forecasting Mechanism Factories 82
3.2.1 Are Statistical Measures of Risk Solve Solvency II? 82
3.2.2 Fractals, Black Swans and Black Duals 83
3.2.3 Trends and Fluctuations in Nonstandard Analysis 84
3.2.4 Analytical Factories 85
3.3 The Legacy of Ingenhousz 86
3.3.1 Stochastic Uncertainty 87
3.3.2 Tychastic Uncertainty 88
3.3.3 Contingent Uncertainty and Its Redundancy 90
3.3.4 Impulse Contingent Uncertainty: Anticipation 91
3.3.5 Correcting Stochastic Systems by Tychastic Systems 91
Part IIMathematical Proofs 95
4 Why Viability Theory? A Survival Kit 96
4.1 Regulated Tychastic Systems 98
4.1.1 Tychastic Systems 98
4.1.2 Tubular Invariant Kernels and Absorption Basins 98
4.1.3 Viability Risk Measures Under Tychastic Systems 100
4.1.4 Regulated Tychastic Systems 101
4.1.5 Viability Risk Measures Under Regulated Tychastic Systems 103
4.2 Graphical Derivatives of Tubes 103
5 General Viabilist Portfolio Performance and Insurance Problem 106
5.1 Tychastic Viability Portfolio Insurance 106
5.1.1 The Data 106
5.1.2 Derivatives of Interval Valued Tubes 108
5.1.3 The Insurance and Performance Problem 110
5.2 Mathematical Metaphors of the VPPI Management Rule 113
5.2.1 Construction of the VPPI Management Rule 116
5.2.2 Sketch of the Proof 117
5.3 Viability Multipliers to Manage Order Books 120
5.3.1 Order Books 120
5.3.2 Transaction Time Function 121
5.3.3 Order Books Dynamics 122
5.3.4 The Viability Solution 123
References 125
Author Index 133
Subject Index 135