Cizek / Härdle / Weron Statistical Tools for Finance and Insurance

2005
ISBN: 978-3-540-27395-0
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 509 Seiten, eBook

Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. The electronic edition, allowing the reader to run, modify, and enhance all quantlets on the spot, can be downloaded at no cost via the attached license registration card.

Zielgruppe

Research

Autoren/Hrsg.

Cizek, P.

Härdle, W.

Weron, W.

Cizek, Pavel

Härdle, Wolfgang Karl

Weron, Rafal

Inhaltsverzeichnis

Finance: Stable Distributions in Finance (Sz. Borak, W. Härdle, R. Weron).- Tail Dependence (R. Schmidt).- Fuzzy Identification Model (N.A. Achsani, H. Sofyan).- Implied Trinomial Tress (K. Komrad).- Nonparametric Productivity Analysis (W.Härdle, S-O. Jeong).- The Exact LR Test of the Scale in the Gamma Family (M. Stehlik).- Pricing of Catastrophe (CAT) Bonds (K. Burnecki, D. Taylor).- Extreme Value Theory - Modeling and Financial Applications (K. Jajuga, D. Papla).- Long Memory for VOLA Surfaces (R. Deo, W. Härdle).- Correlated Asset Risks and Option Pricing (W. Härdle).
Insurance: Loss Distributions (K. Burnecki, G. Kukla, R. Weron).- Visualization of the Risk Process (P. Mista, R. Weron).- Approximation of Ruin Probability (K. Burnecki, P. Mista, A. Weron).- Deductibles (K. Burnecki, J. Nowicka-Zagrajek, A. Weron).- Net Premiums (K. Brunecki, J. Nowicka-Zagrajek).- Premium Calculation in the Collective Risk Model Framework under Different Models of Dependent Claims (W. Otto).- Stable Levy Motion Approximation in Collective Risk Theory (H. Furrer, Z. Michna, A. Weron).- Diffusion Approximation in Risk Theory (Z. Michna).

Leseproben

18 Premiums in the Individual and Collective Risk Models (p.407)

Jan Iwanik and Joanna Nowicka-Zagrajek
The premium is the price for the good "insurance" sold by an insurance company. The right pricing is vital since too low a price level results in a loss, while with too high prices a company can price itself out of the market. It is the actuary’s task to and methods of premium calculation (also called premium calculation principles), i.e. rules saying what premium should be assigned to a given risk.

We present the most important types of premiums in Section 18.1; for more premium calculation principles, that are not considered here, see Straub (1988) and Young (2004). We focus on the monetary payout made by the insurer in connection with insurable losses and we ignore premium loading for expenses and profit.

The goal of insurance modeling is to develop a probability distribution for the total amount paid in bene.ts. This allows the insurance company to manage its capital account and honor its commitments. Therefore, we describe two standard models: the individual risk model in Section 18.2 and the collective risk model in Section 18.3. In both cases, we determine the expectation and variance of the portfolio, consider the approximation of the distribution of the aggregate claims, and present formulae for the considered premiums. It is worth mentioning here that the collective risk model can also be applied to quantifying regulatory capital for operational risk, for example to model a yearly operational risk variable (Embrechts, Furrer, and Kaufmann, 2003).