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Financial and Insurance Formulas

:	Tomas Cipra
:	Financial and Insurance Formulas
:	Physica-Verlag
:	9783790825930
:	1
:	CHF 126.30
:

:	Allgemeines, Lexika
:	English

:	418
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Contents	6
	List of Symbols	12
	1 Introduction	15
	Part I Financial Formulas	17
	2 Simple Interest and Discount	18
	2.1 Simple Interest	18
	2.2 Calendar Conventions	20
	2.3 Simple Interest with Principals Credited mthly	22
	2.4 Simple Discount	22
	Further Reading	23
	3 Compound Interest and Discount	24
	3.1 Compound Interest	24
	3.2 Compound Discount	25
	3.3 Compound Interest and Discount Convertible mthly	26
	3.4 Combination of Simple and Compound Interest	28
	Further Reading	29
	4 Continuous Interest and Discount	30
	Further Reading	32
	5 Classical Analysis of Interest Rates	33
	5.1 Risk-Free Interest Rate and Real Interest Rate	33
	5.2 Term Structure of Interest Rates	35
	Further Reading	36
	6 Systems of Cash Flows	37
	6.1 Present and Future Value	37
	6.2 Internal Rate of Return	40
	6.3 Payback Period	42
	6.4 Duration	42
	6.5 Convexity	45
	Further Reading	46
	7 Annuities	47
	7.1 Annuity Calculus	48
	7.2 Dynamic Annuities	52
	7.3 Annuities Payable mthly	56
	7.4 Continuously Payable Annuities	57
	7.5 Amortization of Debt	58
	Further Reading	60
	8 Depreciation	62
	Further Reading	64
	9 Financial Instruments	65
	9.1 Discount Securities	65
	9.2 Bonds	67
	9.3 Stocks	75
	9.4 Currencies	81
	Further Reading	81
	10 Derivative Securities	83
	10.1 General Classification	83
	10.2 Forwards	84
	10.3 Futures	88
	10.4 Swaps	90
	10.5 Options	91
	Further Reading	99
	11 Utility Theory	100
	Further Reading	102
	12 Rate of Return and Financial Risk	103
	12.1 Rate of Return	103
	12.2 Financial Risk	106
	12.3 Value at Risk VaR	110
	12.4 Credit at Risk CaR	113
	Further Reading	115
	13 Portfolio Analysis and CAPM Model	116
	13.1 Construction of Portfolio	116
	13.2 Portfolio with a Risk-Free Asset	121
	13.3 CAPM Model	123
	Further Reading	125
	14 Arbitrage Theory	126
	Further Reading	129
	15 Financial Stochastic Analysis	130
	15.1 Wiener Process in Finance	130
	15.2 Poisson Process in Finance	132
	15.3 Ito Stochastic Integral	133
	15.4 Stochastic Differential Equations SDE	135
	15.5 Itos Lemma	136
	15.6 Girsanov Theorem on Equivalent Martingale Probability	137
	15.7 Theorem on Martingale Representation	139
	15.8 Derivatives Pricing by Means of Equivalent Martingale Probabilities	139
	15.9 Derivatives Pricing by Means of Partial Differential Equations PDE	141
	15.10 Term Structure Modeling	142
	Further Reading	146
	Part II Insurance Formulas	147
	16 Insurance Classification	148
	Further Reading	153
	17 Actuarial Demography	154
	17.1 Selected Population Indicators	154
	17.2 Life Tables	158
	17.3 Mortality and Survival Modeling	162
	17.4 Multiple Decrement Models	166
	17.5 Multiple Life Functions	167
	17.6 Commutation Functions	167
	Further Reading	169
	18 Classical Life Insurance	170
	18.1 Basic Concepts of Life Insurance	170
	18.2 Symbols and Calculation Principles of Life Insurance	172
	18.3 Technical Provisions in Life Insurance	175
	18.4 Pure Endowments	179
	18.5 Whole Life and Term Insurance	180
	18.6 Further Products of Capital Life Insurance	185
	18.7 Life Annuities	188
	18.8 Multiple Life Insurance	194
	18.9 Premium Reserve and Its Implications	195
	18.10 Medical Underwriting	197
	Further Reading	198
	19 Modern Approaches to Life Insurance	200
	19.1 Critical Illness Insurance	200
	19.2 Flexible Products of Life Insurance	202
	19.3 Unit Linked	203
	19.4 Profit Testing	206
	19.5 Embedded Value	208
	19.6 Fair Value	210
	Further Reading	212
	20 Pension Insurance	213
	20.1 Basic Concepts of Pension Insurance	213
	20.2 Defined Contribution Plan	215
	20.3 Defined Benefit Plan	217
	Further Reading	221
	21 Classical Non-Life Insurance	222
	21.1 Basic Concepts of Non-Life Insurance	222
	21.2 Premium Calculations in Non-Life Insurance	225
	21.3 Forms of Non-Life Insurance and Deductibles	228
	21.4 Technical Provisions in Non-Life Insurance	231
	21.5 Bonus-Malus Systems	236
	Further Reading	237
	22 Risk Theory in Insurance	238
	22.1 Collective Risk Model	238
	22.2 Aggregate Claim Distribution	241
	22.3 Copula	245
	22.4 Credibility Premium	246
	22.5 Ruin Probability	249
	22.6 Deductible	251
	22.7 Calculations for Bonus-Malus Systems	253
	Further Reading	255
	23 Health Insurance	257
	Further Reading	259
	24 Reinsurance	260
	24.1 Basic Concepts of Reinsurance	260
	24.2 Types of Reinsurance	262
	24.3 Solvency	268
	24.4 Alternative Risk Transfer ART	270
	Further Reading	272
	Part III Formulas of Related Disciplines	274
	25 Mathematical Compendium	275
	25.1 Powers with Integral Exponents	275
	25.2 Roots of Real Numbers	275
	25.3 Powers with Rational Exponents	275
	25.4 Powers with Real Exponents	276
	25.5 Formulas an ±