Statistical Tools for Finance and Insurance
Description
Statistical Tools in Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit.
Covering topics such as heavy tailed distributions, implied trinomial trees, support vector machines, valuation of mortgage-backed securities, pricing of CAT bonds, simulation of risk processes and ruin probability approximation, the book does not only offer practitioners insight into new methods for their applications, but it also gives theoreticians insight into the applicability of the stochastic technology. Additionally, the book provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations.
Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. The design of the text links theory and computational tools in an innovative way. All Quantlets for the calculation of examples given in the text are supported by the academic edition of XploRe and may be executed via XploRe Quantlet Server (XQS). The downloadable electronic edition of the book enables one to run, modify, and enhance all Quantlets on the spot.
Reviews / Votes
From the reviews of the first edition:
"This book is designed for students, researchers and practitioners who want to be introduced to modern statistical tools applied in finance and insurance. . The text is comprehensible for a graduate student in financial engineering as well as for an inexperienced newcomer to quantitative finance and insurance who wants to get a grip on advanced statistical tools applied in these fields. An experienced reader . will hopefully enjoy the various computational tools." (Edward M. Psyadlo, Zentralblatt MATH, Vol. 1078, 2006)
"The book under review provides a comprehensive collection of articles on modern quantitative analysis in finance and insurance. In particular . use of formulas and its illustrative examples are attractive to the intended audience." (Dr. Mathias Fischer, Statistical Papers, Vol. 48, 2006)
"The present book, written by Wolfgang Härdle and some of his collaborators, is a welcome addition to the literature in this area. . The book covers a wide range of topical and useful ground. It has plenty of data analysis, plenty of graphics and plenty of references, most of them recent standard texts or recent research contributions or reprints. It will certainly be useful for its intended audience and is worth having for the range of topics and the references alone." (N. H. Bingham, Significance, Vol. 3 (3), 2006)
"This book offers a unique combination of topics from which every market analyst and risk manager will benefit. . the book does not only offers practitioners insight into new methods for their applications, but it also gives theoreticians insight into the applicability of the stochastic technology. . Written in an accessible and engaging style, this self-instructional book makes a good use of extensive examples and full explanations. The design of the text links theory and computational tools in an innovative way." (Zeitschrift für die gesamteVersicherungswissenschaft, Issue 1, 2006)
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Content
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).
