Non-life insurance mathematics. An introduction with stochastic processes.

DOI10.1007/3-540-44889-6zbMath1033.91019OpenAlexW2161830147MaRDI QIDQ1412419

Thomas Mikosch

Publication date: 25 November 2003

Published in: Universitext (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/3-540-44889-6

zbMATH Keywords

Bayes estimationruin theorycollective risk modelindividual risk modelLundberg inequalityBühlmann-Straub modelNon-life insurance

Mathematics Subject Classification ID

Related Items (45)

Bi-seasonal discrete time risk model ⋮ Recovery process model ⋮ Second-order asymptotics of ruin probabilities for semiexponential claims ⋮ Nonparametric analysis of aggregate loss models ⋮ Mixed Poisson process with Pareto mixing variable and its risk applications ⋮ Improved Asymptotics for Ruin Probabilities ⋮ Oracle inequalities for the stochastic differential equations ⋮ Gaussian risk models with financial constraints ⋮ Optimal control of investment, premium and deductible for a non-life insurance company ⋮ Extremes of asymptotically spherical and elliptical random vectors ⋮ Moment and polynomial bounds for ruin-related quantities in risk theory ⋮ Tauberian theorems and large deviations ⋮ The stability of the probability of ruin ⋮ Spatial modelling of claim frequency and claim size in non-life insurance ⋮ Modeling and pricing cyber insurance. Idiosyncratic, systematic, and systemic risks ⋮ On unattainable boundary of a diffusion process range: semi-Markov approach ⋮ A generalization of Panjer's recursion and numerically stable risk aggregation ⋮ Pricing cumulative loss derivatives under additive models via Malliavin calculus ⋮ Approximation of the tail probability of dependent random sums under consistent variation and applications ⋮ Itô calculus for Cramér-Lundberg model ⋮ Stochastic processes with proportional increments and the last-arrival problem ⋮ Alarm system for insurance companies: a strategy for capital allocation ⋮ An optimal investment strategy with maximal risk aversion and its ruin probability in the presence of stochastic volatility on investments ⋮ EXPANSION IN BELL POLYNOMIALS OF THE DISTRIBUTION OF THE TOTAL CLAIM AMOUNT WITH WEIBULL-DISTRIBUTED CLAIM SIZES ⋮ Ruin problem of a two-dimensional fractional Brownian motion risk process ⋮ Regular variation of a random length sequence of random variables and application to risk assessment ⋮ On the Gerber-Shiu discounted penalty function for subexponential claims ⋮ Ruin probability in the presence of risky investments ⋮ A saddlepoint approximation to the distribution of inhomogeneous discounted compound Poisson processes ⋮ Estimation of Tails and Related Quantities Using the Number of Near-Extremes ⋮ ON THE IMPACT OF HIDDEN TRENDS FOR A COMPOUND POISSON MODEL WITH PARETO-TYPE CLAIMS ⋮ Explicit Solution Processes for Nonlinear Jump-Diffusion Equations ⋮ On the asymptotic distribution of certain bivariate reinsurance treaties ⋮ RUIN PROBABILITY FOR HYPO-EXPONENTIAL CLAIM IN CLASSICAL RISK PROCESS WITH REINSURANCE ⋮ Compound Poisson approximation to convolutions of compound negative binomial variables ⋮ Tail behaviour of random sums under consistent variation with applications to the compound renewal risk model ⋮ A parametric model fitting time to first event for overdispersed data: application to time to relapse in multiple sclerosis ⋮ Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators ⋮ Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler? ⋮ Robust adaptive efficient estimation for semi-Markov nonparametric regression models ⋮ PORTFOLIO ALLOCATION IN A LEVY-TYPE JUMP-DIFFUSION MODEL WITH NONLIFE INSURANCE RISK ⋮ Recovery process model for two companies ⋮ Variance Optimal Stopping for Geometric Lévy Processes ⋮ Diagonal effects in claims reserving ⋮ Prediction of outstanding payments in a Poisson cluster model

This page was built for publication: Non-life insurance mathematics. An introduction with stochastic processes.