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Buhlmann H., Berger M. (Ed) — Mathematical Methods in Risk Theory
Buhlmann H., Berger M. (Ed) — Mathematical Methods in Risk Theory



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Название: Mathematical Methods in Risk Theory

Авторы: Buhlmann H., Berger M. (Ed)

Аннотация:

"... a masterful work.." Transactions, Soc of Actuaries Meetings 65

"The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments of the field. It will be of great interest to the actuary as well as to the statistician who wants to become familiar with the subject." Math. Reviews Vol. 43

"..., the book (and its author) had enormous impact on the development of risk theory. It was the first self-contained monograph on risk theory providing a rigorous probabilistic foundation. ...[and]... made an important contribution to the successful development of risk theory. This success has made the book a classic." Zentralblatt MATH, 1996


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1996

Количество страниц: 210

Добавлена в каталог: 03.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $a_0$      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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