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Risk Theory : the Stochastic Basis of Insurance

Author: R E Beard; Teivo Pentikäinen; E Pesonen
Publisher: Dordrecht : Springer Netherlands, 1984.
Series: Monographs on statistics and applied probability (Series), 20.
Edition/Format:   eBook : Document : English : Third editionView all editions and formats
Summary:
The theory of risk already has its traditions. A review of its classical results is contained in Bohlmann (1909). This classical theory was associated with life insurance mathematics, and dealt mainly with deviations which were expected to be produced by random fluctua tions in individual policies. According to this theory, these deviations are discounted to some initial instant; the square root of the sum of the  Read more...
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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  Read more...

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