LEADER 05486nam 2200697Ia 450 001 9910877996603321 005 20200520144314.0 010 $a9786612307928 010 $a0-470-31788-4 010 $a1-282-30792-4 010 $a0-470-86042-1 010 $a0-470-31704-3 010 $a0-585-27223-9 035 $a(CKB)111004366690922 035 $a(EBL)470348 035 $a(SSID)ssj0000251581 035 $a(PQKBManifestationID)11201091 035 $a(PQKBTitleCode)TC0000251581 035 $a(PQKBWorkID)10171139 035 $a(PQKB)11337156 035 $a(MiAaPQ)EBC470348 035 $a(OCoLC)264615393 035 $a(PPN)159315506 035 $a(EXLCZ)99111004366690922 100 $a19980922d1999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aStochastic processes for insurance and finance /$fTomasz Rolski ... [et al.] 210 $aChicester $cJ. Wiley$d1999 215 $a1 online resource (683 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-471-95925-1 320 $aIncludes bibliographical references (p. [617]-638) and index. 327 $aStochastic Processes for Insurance and Finance; Contents; Preface; List of Principal Notation; 1 Concepts from Insurance and Finance; 1.1 Introduction; 1.2 The Claim Number Process; 1.2.1 Renewal Processes; 1.2.2 Mixed Poisson Processes; 1.2.3 Some Other Models; 1.3 The Claim Size Process; 1.3.1 Dangerous Risks; 1.3.2 The Aggregate Claim Amount; 1.3.3 Comparison of Risks; 1.4 Solvability of the Portfolio; 1.4.1 Premiums; 1.4.2 The Risk Reserve; 1.4.3 Economic Environment; 1.5 Reinsurance; 1.5.1 Need for Reinsurance; 1.5.2 Types of Reinsurance; 1.6 Ruin Problems; 1.7 Related Financial Topics 327 $a1.7.1 Investment of Surplus1.7.2 Diffusion Processes; 1.7.3 Equity Linked Life Insurance; 2 Probability Distributions; 2.1 Random Variables and Their Characteristics; 2.1.1 Distributions of Random Variables; 2.1.2 Basic Characteristics; 2.1.3 Independence and Conditioning; 2.1.4 Convolution; 2.1.5 Transforms; 2.2 Parametrized Families of Distributions; 2.2.1 Discrete Distributions; 2.2.2 Absolutely Continuous Distributions; 2.2.3 Parametrized Distributions with Heavy Tail; 2.2.4 Operations on Distributions; 2.2.5 Some Special Functions; 2.3 Associated Distributions 327 $a2.4 Distributions with Monotone Hazard Rates2.4.1 Discrete Distributions; 2.4.2 Absolutely Continuous Distributions; 2.5 Heavy-Tailed Distributions; 2.5.1 Definition and Basic Properties; 2.5.2 Subexponential Distributions; 2.5.3 Criteria for Subexponentiality and the Class S'; 2.5.4 Pareto Mixtures of Exponentials; 2.6 Detection of Heavy-Tailed Distributions; 2.6.1 Large claims; 2.6.2 Quantile Plots; 2.6.3 Mean Residual Hazard Function; 2.6.4 Extreme Value Statistics; 3 Premiums and Ordering of Risks; 3.1 Premium Calculation Principles; 3.1.1 Desired Properties of "Good" Premiums 327 $a3.1.2 Basic Premium Principles3.1.3 Quantile Function: Two More Premium Principles; 3.2 Ordering of Distributions; 3.2.1 Concepts of Utility Theory; 3.2.2 Stochastic Order; 3.2.3 Stop-Loss order; 3.2.4 The Zero Utility Principle; 3.3 Some Aspects of Reinsurance; 4 Distributions of Aggregate Claim Amount; 4.1 Individual and Collective Model; 4.2 Compound Distributions; 4.2.1 Definition and Elementary Properties; 4.2.2 Three Special Cases; 4.2.3 Some Actuarial Applications; 4.2.4 Ordering of Compounds; 4.2.5 The Larger Claims in the PortfoIio; 4.3 Claim Number Distributions 327 $a4.3.1 Classical Examples Panjer's Recurrence Relation; 4.3.2 Discrete Compound Poisson Distributions; 4.3.3 Mixed Poisson Distributions; 4.4 Recursive Computation Methods; 4.4.1 The Individual Model: De Pril's Algorithm; 4.4.2 The Collective Model: Panjer's Algorithm; 4.4.3 A Continuous Version of Panjer's Algorithm; 4.5 Lundberg Bounds; 4.5.1 Geometric Compounds; 4.5.2 More General Compound Distributions; 4.5.3 Estimation of the Adjustment Coefficient; 4.6 Approximation by Compound Distributions; 4.6.1 The Total Variation Distance; 4.6.2 The Compound Poisson Approximation 327 $a4.6.3 Homogeneous Portfolio 330 $aStochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address:The principal concepts from insurance and financePractical examples with real life dataNumerical and algorit 410 0$aWiley series in probability and statistics. 606 $aInsurance$xMathematical models 606 $aFinance$xMathematical models 606 $aStochastic processes 615 0$aInsurance$xMathematical models. 615 0$aFinance$xMathematical models. 615 0$aStochastic processes. 676 $a332 676 $a368.015192 701 $aRolski$b Tomasz$0103667 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877996603321 996 $aStochastic processes for insurance and finance$94186048 997 $aUNINA