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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
R E Beard; Teivo Pentikäinen; E Pesonen |

ISBN: | 9789401176804 9401176809 |

OCLC Number: | 851369964 |

Description: | 1 online resource (xvii, 408 pages). |

Contents: | 1 Definitions and notation -- 1.1 The purpose of the theory of risk -- 1.2 Stochastic processes in general -- 1.3 Positive and negative risk sums -- 1.4 Main problems -- 1.5 On the notation -- 1.6 The moment generating function, the characteristic function, and the Laplace transform -- 2 Claim number process -- 2.1 Introduction -- 2.2 The Poisson process -- 2.3 Discussion of conditions -- 2.4 Some basic formulae -- 2.5 Numerical values of Poisson probabilities -- 2.6 The additivity of Poisson variables -- 2.7 Time-dependent variation of risk exposure -- 2.8 Formulae concerning the mixed Poisson distribution -- 2.9 The Polya process -- 2.10 Risk exposure variation inside the portfolio -- 3 Compound Poisson process -- 3.1 The distribution of claim size -- 3.2 Compound distribution of the aggregate claim -- 3.3 Basic characteristics of F -- 3.4 The moment generating function -- 3.5 Estimation of S -- 3.6 The dependence of the S function on reinsurance -- 3.7 Decomposition of the portfolio into sections -- 3.8 Recursion formula for F -- 3.9 The normal approximation -- 3.10 Edgeworth series -- 3.11 Normal power approximation -- 3.12 Gamma approximation -- 3.13 Approximations by means of functions belonging to the Pearson family -- 3.14 Inversion of the characteristic function -- 3.15 Mixed methods -- 4 Applications related to one-year time-span -- 4.1 The basic equation -- 4.2 Evaluation of the fluctuation range of the annual underwriting profits and losses -- 4.3 Some approximate formulae -- 4.4 Reserve funds -- 4.5 Rules for the greatest retention -- 4.6 The case of several Ms -- 4.7 Excess of loss reinsurance premium -- 4.8 Application to stop loss reinsurance -- 4.9 An application to insurance statistics -- 4.10 Experience rating, credibility theory -- 5 Variance as a measure of stability -- 5.1 Optimum form of reinsurance -- 5.2 Reciprocity of two companies -- 5.3 Equitability of safety loadings: a link to theory of multiplayer games -- 6 Risk processes with a time-span of several years -- 6.1 Claims -- 6.2 Premium income P(1, t) -- 6.3 Yield of investments -- 6.4 Portfolio divided in sections -- 6.5 Trading result -- 6.6 Distribution of the solvency ratio u -- 6.7 Ruin probability?T(u), truncated convolution -- 6.8 Monte Carlo method -- 6.9 Limits for the finite time ruin probability?T -- 7 Applications related to finite time-span T -- 7.1 General features of finite time risk processes -- 7.2 The size of the portfolio -- 7.3 Evaluation of net retention M -- 7.4 Effect of cycles -- 7.5 Effect of the time-span T -- 7.6 Effect of inflation -- 7.7 Dynamic control rules -- 7.8 Solvency profile -- 7.9 Evaluation of the variation range of u(t) -- 7.10 Safety loading -- 8 Risk theory analysis of life insurance -- 8.1 Cohort analysis -- 8.2 Link to classic individual risk theory -- 8.3 Extensions of the cohort approach -- 8.4 General system -- 9 Ruin probability during an infinite time period -- 9.1 Introduction -- 9.2 The infinite time ruin probability -- 9.3 Discussion of the different methods -- 10 Application of risk theory to business planning -- 10.1 General features of the models -- 10.2 An example of risk theory models -- 10.3 Stochastic dynamic programming -- 10.4 Business objectives -- 10.5 Competition models -- Appendixes -- A Derivation of the Poisson and mixed Poisson processes -- B Edgeworth expansion -- C Infinite time ruin probability -- D Computation of the limits for the finite time ruin probability according to method of Section 6.9 -- E Random numbers -- F Solutions to the exercises -- Author index. |

Series Title: | Monographs on statistics and applied probability (Series), 20. |

Responsibility: | by Robert Eric Beard, Teivo Pentikäinen, Erkki Pesonen. |

### Abstract:

The theory of risk already has its traditions. Further, non-life insurance, to which risk theory has, in fact, its most rewarding applications, was mainly outside the field of interest of the risk theorists.
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