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Oft nutzen Händler einen Produktkonfigurator Was ist eCommerce? mehr und mehr dreht sich alles um das World Wide Web Geldbeutel 523 517Index 501References exercises to 499Answers Mixtures 495A.13 Convolution 489A.12 distributions standard Some 487A.11 functions generating Probability 486A.10 functions generating Moment 485A.9 variables random for independence and Conditioning 483A.8 distributions Joint 482A.7 function distribution the of terms in Expectation 481A.6 moments and Expectations 480A.5 Distributions 479A.4 variables Random 479A.3 independence and Conditioning 477A.2 measures probability and spaces Sample 477A.1 theory probability of review A 473Appendix 473Exercises References and 469Notes Estimation 46524.7 exactness for Conditions 46224.6 Approximations 45924.5 examples Classical 45724.4 credibility Bayesian for framework General 45324.3 variable random another to respect with variance and expectation Conditional 44924.2 material Introductory 44924.1 theory Credibility 44524 445Exercises references and 441Notes loss aggregate maximal The 43823.7 process surplus Poisson compound The 43423.6 formulas Recursion 43323.5 ruin at deficit the of Distribution 42423.4 theory ruin to approach martingale The 42223.3 approach equation functional A 42023.2 Introduction 42023.1 models Ruin 41723 417Exercises references and 412Notes adequacy capital for measures Risk 40822.5 method comparison general A 40622.4 inequality Jensen's functions: concave and Convex 40322.3 theory Utility 40322.2 Introduction 40322.1 assessment Risk 39822 398Exercises references and 393Notes S for formula recursion A 38821.11 modifications other and Deductibles 38721.10 distributions Poisson compound two of sum The 38521.9 type particular a of claims Counting 38421.8 0 at mass point the Handling 38321.7 distribution severity a Choosing 38121.6 distribution frequency a Choosing 38121.5 S of distribution Exact 38021.4 functions Generating 37921.3 S of variance and mean The 37721.2 Introduction 37721.1 distributions Compound 37521 THEORY RISK IV 373Part 372Exercises references and 364Notes markets Bond 36120.13 formula Black-Scholes-Merton The 35820.12 markets of Completeness 35320.11 measures neutral risk of uniqueness and Existence 35120.10 condition Arbitrage-free 34820.9 market financial general A 34620.8 options American 34220.7 model binomial multi-period The 33920.6 model binomial one-period the in prices Option 33720.5 contracts Option 33420.4 Arbitrage 33320.3 markets financial in prices Modelling 33320.2 Introduction 33320.1 Markets Financial of Mathematics the to Introduction 32920 328Exercises references and 328Notes models Semi-Markov 32719.6 models multi-state in testing Profit 32419.5 reserves multi-state for equations differential and Recursion 31119.4 model continuous-time The 30519.3 model discrete-time The 30419.2 Introduction 30419.1 models Multi-state 30019 299Exercises references and 295Notes motion Brownian 29318.7 processes Poisson 29318.6 processes time continuous to Introduction 28718.5 chains Markov Finite-state 28618.4 Martingales 28318.3 chains Markov 28118.2 Introduction 28118.1 processes stochastic to introduction An 27918 MODELS STOCHASTIC ADVANCED III 276Part 276Exercises references and 273Notes Copulas 27117.7 model shock common The 27017.6 problems Other 26117.5 (T,J) of distribution joint The 26117.4 T of distribution The 25917.3 distributions Joint 25917.2 Introduction 25917.1 time failure minimum The 25617 254Exercises examples benefit non-level Some 25216.5 distributions Exact 25016.4 case discrete the in calculations Variance 24816.3 case continuous the in calculations Variance 24816.2 Introduction 24816.1 contracts benefit level under Simplifications 24416 244Exercises references and 243Notes terminology and notation Standard 24115.8 rL of variance The 23515.7 premiums to approach stochastic The 23315.6 reserves to approach stochastic The 23315.5 contracts Deferred 22915.4 benefits annuity to approach stochastic The 22515.3 benefits insurance to approach stochastic The 22415.2 Introduction 22415.1 annuities and insurance to approach stochastic The 22215 222Exercises references and 221Notes rates interest Stochastic 22014.9 model stochastic the in expectancy Life 21914.8 table life stochastic The 21714.7 approximation standard The 21614.6 distributions Shifted 21514.5 Examples 21314.4 case continuous The 21214.3 case discrete The 21114.2 distributions survival to Introduction 21114.1 times failure and distributions Survival 20914 MODEL CONTINGENCIES LIFE STOCHASTIC THE II 207Part 204Exercises plans Pension 20313.3 annuities Variable 19913.2 life Universal 19913.1 topics Specialized 19613 196Exercises references and 189Notes measurement Profit 18712.4 calculations balance and reserve Realistic 18612.3 reserves on Effect 18412.2 Introduction 18412.1 Profits and Expenses 18112 181Exercises references and 175Notes tables single-decrement Associated 17111.7 analogy machine A 17111.6 statuses joint-life with analogy The 17011.5 decrement of forces the from model the Determining 16911.4 Insurances 16611.3 model basic The 16611.2 Introduction 16611.1 theory Multiple-decrement 16111 161Exercises references and 161Notes applications Spreadsheet 16010.12 terminology and notation Standard 15910.11 risk credit annuity to Applications 15610.10 problems Duration 15310.9 insurances Contingent 15210.8 contract insurance two-life general The 15010.7 contract annuity two-life general The 14910.6 insurances death of Moment 14710.5 insurances and annuities Last-survivor 14610.4 insurances and annuities Joint-life 14410.3 status joint-life The 14410.2 Introduction 14410.1 contracts Multiple-life 14210 142Exercises remarks Further 1419.5 tables annuity in Projections 1399.4 formulas in Changes 1389.3 tables ultimate and Select 1379.2 Introduction 1379.1 mortality Select 1329 132Exercises references and 131Notes terminology and notation actuarial Standard 1298.12 table life the from approximations Further 1258.11 calculation exact of examples Some 1248.10 reserves for equations Differential 1238.9 case continuous the in identity insurance-annuity general The 1228.8 reserves and Premiums 1198.7 death of moment the at payable Insurances 1188.6 mortality of force The 1158.5 annuities life Continuous 1148.4 case interest constant The 1138.3 discount of force The 1128.2 annuities continuous to Introduction 1128.1 payments Continuous 1098 109Exercises terminology and notation Standard 1077.8 durations fractional at Reserves 1067.7 reserves and premiums period Fractional 1057.6 computation and Approximation 1047.5 annuities Immediate paid7.4 annuities Life 997.3 only interest with discounted flows Cash 987.2 Introduction 987.1 durations Fractional 947 93Exercises applications Spreadsheet 916.10 terminology and notation Standard 906.9 formulas paid-up and difference Premium 886.8 reserve the of return a involving Policies 886.7 values Nonforfeiture 876.6 reserves for Bases 836.5 contract annuity or insurance an of analysis Detailed 826.4 Recursion 816.3 reserves of pattern general The 786.2 reserves to Introduction 786.1 reserves annuity and Insurance 746 74Exercises applications Spreadsheet 725.9 terminology and notation Standard 705.8 identity insurance-annuity general A 705.7 formulas of Summary 695.6 annuities as viewed Insurances 645.5 benefits insurance-annuity Combined 645.4 insurance life of Types 615.3 premiums insurance life Calculating 615.2 Introduction 615.1 insurance Life 595 58Exercises calculations Spreadsheet 574.8 terminology and notation Standard 564.7 considerations practical Some 554.6 premiums annual with annuities Deferred 534.5 payments Guaranteed 504.4 function discount survivorship and interest The 484.3 premiums annuity Calculating 474.2 Introduction 474.1 annuities Life 454 45Exercises references and 45Notes table sample A 443.7 terminology and notation Standard 443.6 tables life of Choice 423.5 expectancy Life 413.4 qx of values the from table life the Constructing 403.3 Probabilities 393.2 definitions Basic 393.1 table life The 353 35Exercises references and 34Notes calculations Spreadsheet 332.15 terminology and notation Standard 302.14 structure term and prices Forward 282.13 return of rates Internal 272.12 function discount of Change 262.11 identity splitting the and shifting Time 202.11 reserves and Balances 182.10 flows cash pattern Regular 172.9 notation Vector 132.8 equivalence actuarial and Values 122.7 interest Constant 122.6 rates discount and Interest 112.5 function discount the Calculating 92.4 functions Discount 82.3 currencies with analogy An 72.2 flows Cash 72.1 model deterministic basic The 62 Conclusion 61.6 Reassessment 51.5 equity and Adequacy 51.4 investments and Finance 41.3 models stochastic versus Deterministic 31.2 insurance and Risk 31.1 motivation and Introduction 11 MODEL CONTINGENCIES LIFE DETERMINISTIC THE I xxiiiPart index xxiNotation xviiAcknowledgements Preface 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