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Vector-valued measures --- Decomposition (Mathematics) --- Riesz spaces --- Boolean rings

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Gegenstand der Versicherungsmathematik sind Modelle und Methoden zur Quantifizierung von Risiken in der Versicherungswirtschaft. Die Versicherungsmathematik ist damit ein Teilgebiet der Stochastik mit einer anwendungsspezifischen Ausprägung. Den Schwerpunkt dieses Buches bildet die Mathematik der Schadenversicherung. Aufbauend auf dem individuellen und dem kollektiven Modell für den Gesamtschaden eines Bestandes behandelt es grundlegende Aspekte der Tarifierung und der Schadenreservierung sowie die wichtigsten Formen der Rückversicherung und Methoden zum Vergleich von Risiken. Dabei erweist sich neben dem kollektiven Modell auch das multiplikative Modell als ein Grundstein der Modellierung. Darüber hinaus werden die elementaren Grundlagen der Finanzmathematik und der Lebensversicherung dargestellt und die erforderlichen Hilfsmittel der Stochastik entwickelt.

Public finance. --- Finance. --- Economics, Mathematical . --- Economic theory. --- Public Economics. --- Finance, general. --- Quantitative Finance. --- Economic Theory/Quantitative Economics/Mathematical Methods.

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Stochastic processes --- Functional analysis --- Martingales (Mathematics) --- Set functions. --- Martingales (Mathematics).

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This handbook presents the basic aspects of actuarial loss reserving. Besides the traditional methods, it also includes a description of more recent ones and a discussion of certain problems occurring in actuarial practice, like inflation, scarce data, large claims, slow loss development, the use of market statistics, the need for simulation techniques and the task of calculating best estimates and ranges of future losses. In property and casualty insurance the provisions for payment obligations from losses that have occurred but have not yet been settled usually constitute the largest item on the liabilities side of an insurer's balance sheet. For this reason, the determination and evaluation of these loss reserves is of considerable economic importance for every property and casualty insurer. Actuarial students, academics as well as practicing actuaries will benefit from this overview of the most important actuarial methods of loss reserving by developing an understanding of the underlying stochastic models and how to practically solve some problems which may occur in actuarial practice.

Actuarial science. --- Statistics . --- Insurance. --- Actuarial Sciences. --- Statistical Theory and Methods. --- Statistics for Business, Management, Economics, Finance, Insurance.

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This handbook presents the basic aspects of actuarial loss reserving. Besides the traditional methods, it also includes a description of more recent ones and a discussion of certain problems occurring in actuarial practice, like inflation, scarce data, large claims, slow loss development, the use of market statistics, the need for simulation techniques and the task of calculating best estimates and ranges of future losses. In property and casualty insurance the provisions for payment obligations from losses that have occurred but have not yet been settled usually constitute the largest item on the liabilities side of an insurer's balance sheet. For this reason, the determination and evaluation of these loss reserves is of considerable economic importance for every property and casualty insurer. Actuarial students, academics as well as practicing actuaries will benefit from this overview of the most important actuarial methods of loss reserving by developing an understanding of the underlying stochastic models and how to practically solve some problems which may occur in actuarial practice.

Actuarial science. --- Statistics . --- Insurance. --- Actuarial Sciences. --- Statistical Theory and Methods. --- Statistics for Business, Management, Economics, Finance, Insurance.