This survey contains more than 3,000 formulas and methods from the field of finance and insurance mathematics (as well as related formulas in mathematics, probability theory, statistics, econometrics, index numbers, demography, stochastic processes and time series). The formulas are mostly applicable in financial and actuarial practice. Their mathematical level ranges from simple ones based on arithmetic to very sophisticated matters of higher mathematics (e. g. stochastic calculus), but they are usually presented in the form most frequently used in applications. Explanations and references to related parts of the survey are given so that one can easily browse and look them up in the text; the detailed Index is also helpful for this purpose. The survey will be of benefit for students, researchers and practitioners in finance and insurance.

Zusammenfassung
Financial and insurance calculations become more and more frequent and helpful for many users not only in their profession life but sometimes even in their personal life. Therefore a survey of formulas of ?nancial and insurance mathematics that can be applied to such calculations seems to be a suitable aid. In some cases one should use instead of the term formula more suitable terms of the type method, p- cedure or algorithm since the corresponding calculations cannot be simply summed up to a single expression, and a verbal description without introducing complicated symbols is more appropriate. The survey has the following ambitions: • The formulas should be applicable in practice: it has motivated their choice for this survey ?rst and foremost. On the other hand it is obvious that by time one puts to use in practice seemingly very abstract formulas of higher mathematics, e.g. when pricing ?nancial derivatives, evaluating ?nancial risks, applying accou- ing principles based on fair values, choosing alternative risk transfers ARL in insurance, and the like. • The formulas should be error-free (though such a goal is not achievable in full) since in the ?nancial and insurance framework one publishes sometimes in a h- tic way various untried formulas and methods that may be incorrect. Of course, the formulas are introduced here without proofs because their derivation is not the task of this survey.

Inhalt
Financial Formulas.- Simple Interest and Discount.- Compound Interest and Discount.- Continuous Interest and Discount.- Classical Analysis of Interest Rates.- Systems of Cash Flows.- Annuities.- Depreciation.- Financial Instruments.- Derivative Securities.- Utility Theory.- Rate of Return and Financial Risk.- Portfolio Analysis and CAPM Model.- Arbitrage Theory.- Financial Stochastic Analysis.- Insurance Formulas.- Insurance Classification.- Actuarial Demography.- Classical Life Insurance.- Modern Approaches to Life Insurance.- Pension Insurance.- Classical Non-Life Insurance.- Risk Theory in Insurance.- Health Insurance.- Reinsurance.- Formulas of Related Disciplines.- Mathematical Compendium.- Probability Theory.- Descriptive and Mathematical Statistics.- Econometrics.- Index Numbers.- Stochastic Processes.- Statistical Analysis of Time Series.