Risk and insurance a graduate text /: a graduate text. (2020)

• Record Type: Book
• Further Information: Note: Søren Asmussen, Mogens Steffenson.
• Other Names: Asmussen, Søren; Steffensen, Mogens, 1970-
• Contents: Intro -- Preface -- Contents -- Notation -- Internal Reference System -- Special Typeface -- Miscellaneous Mathematical Notation -- Standard Distributions -- Abbreviations -- Chapter I: Basics -- 1 Actuarial Versus Financial Pricing -- 2 Utility -- 3 Premium Rules -- 4 Reinsurance -- 5 Poisson Modelling -- 5.1 The Poisson Distribution as a Binomial Limit -- 5.2 The Poisson Process -- 5.3 Superposition and Thinning -- Chapter II: Experience Rating -- 1 Bayes and Empirical Bayes -- 1.1 The Bayes Premium -- 2 Exponential Families and Conjugate Priors -- 3 Credibility Premiums 3.1 The Simple Credibility Model -- 3.2 The General Credibility Model -- 3.3 The Bühlmann Model -- 3.4 The Bühlmann-Straub Model -- 3.5 Quadratic Loss -- 4 Bonus-Malus Systems -- 4.1 Introduction -- 4.2 Loimaranta Efficiency -- 4.3 Bayes Premiums -- Chapter III: Sums and Aggregate Claims -- 1 Introduction -- 2 Heavy Tails. Subexponential Distributions -- 2.1 Definition of Subexponentiality and Sufficient Conditions -- 2.2 Further Mathematical Properties -- 3 Large Deviations of Sums of Light-Tailed Random Variables -- 3.1 The Cumulant Function -- 3.2 The Legendre-Fenchel Transform 3.3 Exponential Families and Change of Measure -- 3.4 The Chernoff Bound and the Saddlepoint Approximation -- 4 Tails of Sums of Light-Tailed Random Variables -- 5 Aggregate Claims and Compound Sums: Generalities -- 5.1 Poisson Compounding -- 6 Panjer's Recursion -- 7 Tails of Compound Sums -- 7.1 Heavy Tails: The Subexponential Approximation -- 7.2 Light Tails: The Saddlepoint Approximation -- 7.3 The NP Approximation -- Chapter IV: Ruin Theory -- 1 The Cramér-Lundberg Model -- 2 First Results: Martingale Techniques -- 3 Ladder Heights. Heavy Tails -- 4 Proof of the Cramér-Lundberg Approximation 5 Finite Time Ruin Probabilities -- 5.1 Finite Horizon Ruin with Light Tails -- 5.2 Finite Horizon Ruin with Heavy Tails -- 6 Markov Regime Switching -- 6.1 The Averaged Model -- 6.2 The Matrix m.g.f. -- 6.3 Cramér-Lundberg Theory -- 7 Level-Dependent Premiums -- 8 The Diffusion Approximation -- Chapter V: Markov Models in Life Insurance -- 1 The Contract Payments and the Probability Model -- 2 Canonical Models -- 2.1 Mortality Modelling -- 2.2 The Survival Model -- 2.3 The Disability Model -- 2.4 The Spouse Model -- 3 Valuation of the Payments -- 4 Valuation in Canonical Models 4.1 The Survival Model -- 4.2 The Disability Model -- Chapter VI: Financial Mathematics in Life Insurance -- 1 Background and Simple Claims -- 2 Payment Streams -- 3 Unit-Link Insurance -- 4 With-Profit Insurance and the Dynamics of the Surplus -- 5 Cash Dividends and Market Reserve -- 6 The Pure Case of Cash Dividends -- 7 Bonus Payments and Market Reserve -- 8 The Pure Case of Bonus Payments -- 9 Comparison of Products -- Chapter VII: Special Studies in Life Insurance -- 1 Duration-Dependent Intensities and Payments -- 2 Reserve-Dependent Payments and Intensities
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (505 p.)
• Subjects: 368/.01; Insurance -- Mathematics; Insurance -- Mathematics; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030351762; 3030351769; 9783030351779; 3030351777; 9783030351786; 3030351785
• Related ISBNs: 9783030351755; 3030351750
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.