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| Buhlmann H., Berger M. (Ed) — Mathematical Methods in Risk Theory |
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| Предметный указатель |
Absolute retention problem 113
Absolute retention problem, when the risk parameter is known 156
Absolute retention problem, when the risk parameters are drawn from one or more collectives 159
Accumulated claim process 36
Admissible stability policy 135
Ammeter 68
Approximation part 99
Asymptotic formula for  174
Bailey 93
Barrier strategy 168
Beard, Pentikaeinen and Pesonen VII
bernoulli 32
Beta distribution 7 18
Bichsel 65 93 106
Binomial distribution 9 18
Borch 132 165 191 195
Cauchy distribution 8 18
Central moment 16
Characteristic function 20
Chebyshev’s inequality 21
Chintchin 69
Chung 42
Claim amount 3
Claim amount, interoccurrence time 47
Collective premium 88
Compound Poisson 39
Conditional distribution function 25
Conditional distribution function, expectation 25
Contagion models 51
Contingency loading 87
Continuous distribution function 4 201
Covariance 30
Cramer 23 132 141 143
Credibility formula 101
Credibility formula, premium 93
Criterion, the dividend policy 112
Criterion, the dividend policy, the probability of 132
Criterion, the dividend policy, the utility 132
De finetti 113 114 115 132 164 168
De Finetti solution 116
Density function 5
Discrete random walks 145
Distribution function 3
Dividend policy 164
Dividend policy in the continuous case 168
Dividend policy in the discrete case 165
Doob 100
Du Mouchel 192 195
Equivalent evaluations 179
Excess of loss 113
Existence theorem for an equivalent utility 184
Expected value 12
Expected value, part 100
Exponential distribution 6 18
Feller 15 39 44 69 75 144 145 146 147 149
Fluctuation part 99 100
Freed mann 100
Gamma distribution 6 18
Generalized Riemann — Stieltjes integral 12 201
Geometric distribution 11 18
Gerber 151 170 177
Global reinsurance 112
Greenwood and Yule 68
Hofmann 39 58
Homogeneous with respect to the claim amounts 64
Homogeneous with respect to the number of claims 64
Homogeneous with respect to the number of claims and to the claim amounts 64
Independence 28
Individual reinsurance 111
Integrable function 203
Integral evaluation 188
Integral evaluation, instantaneous 189
Integro-differential equation of the barrier strategy 171
Intensity of frequency 43
Jung 60
k-th central moment 16
k-th moment about the origin 16
Kendall 15
Kolmogorov’s (forward) differential equation system 43
| Kupper 54
Law of Large Numbers 32
Levy 69
Logarithmic distribution 11 18
Logarithmic distribution, normal distribution 5 18
Lundberg, F. 132
Lundberg, O. 68 77 93
Markov processes 39
Mayerson 93
Miyasawa 167
Moment about the origin 16
Moment about the origin, generating function 20
Morill 167 168
Multi-dimensional distribution function 22
Negative binomial distribution 11 18
Non-proportional reinsurance 112
Normal distribution 5 18
Number of claims process 36
Operational time 49
Optimum dividend policy 164
Pareto distribution 8 18
Pareto-optimal 191
Parzen 15
Pesonen 75
Philipson VII 39 58
Planning horizon 133
Poisson distribution 10 18
Polya-Eggenberger 53
Portfolio 76
Portfolio, function 76
Premium calculation 85
Premium calculation, function 36
Principles of premium calculation 86
Proportional rcinsurace 112
Quantile 20
Random variable 3
Random variable, walk of the risk carrier’s free reserves 126
Record height 146
Record height, jump 146
Record height, point 146
Reinsurance arrangements 14
Relative retention problem 113
Renewal theory 144
Renewal theory, process 147
Reserves 111 129
Retentions 111
Risk exchange 190
Risk exchange in the collective 63
Risk exchange, collective and credibility premium in automobile liability insurance 106
Risk exchange, premium 87
Risk exchange, process 35
Rozanov 15
Schwartz 100
Seal VII
skewness 16
Stability criteria 131 132
Stability problem 131
Stabilizing in size 77
Stabilizing in time 77
Standard deviation 16
Step distribution function 5 201
Stochastic processes with independent increments 37
Surplus reinsurance 112
Taecklind 143
Takeuchi 167
Thyrion 70 75
Transition probabilities 40
Utility as criterion of stability 178
Utility, axioms about 182
Utility, definition of 179
Utility, kernel 188
Vajda 114
Variance 16
Variance, part 100
Von Neumann, Morgenstern 132 180 182 187 199
Waiting time 47
Weighted laws of probability 65
Weights in the credibility totmulae 103
Wrener — Hopf method 141
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