Finite-time Lundberg inequalities in the Cox case

DOI10.1080/03461238.1993.10413911zbMath0785.62094OpenAlexW2147505451MaRDI QIDQ3142172

Hanspeter Schmidli, Jan Grandell, Paul Embrechts

Publication date: 26 April 1994

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461238.1993.10413911

zbMATH Keywords

insurance companyMarkov chainrisk processCox processpiecewise deterministic Markov processestime of ruinsurplusintensity processconstruction of martingalesestimates for ruin probabilitiesfinite-time Lundberg inequalityMarkov renewal intensity

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Applications of statistics to actuarial sciences and financial mathematics (62P05) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Renewal theory (60K05)

Related Items (20)

Estimation of the Lundberg coefficient for a Markov modulated risk model ⋮ Supermodular Order and Lundberg Exponents ⋮ Ruin theory for the risk process described by PDMPs ⋮ Exponential inequalities for ruin probabilities of risk processes perturbed by diffusion ⋮ Lapse risk in life insurance: correlation and contagion effects among policyholders' behaviors ⋮ Large claims approximations for risk processes in a Markovian environment ⋮ On the typical level crossing time and path ⋮ Cramér-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion ⋮ Modelling of extremal events in insurance and finance ⋮ Contagion modeling between the financial and insurance markets with time changed processes ⋮ Ruin probabilities for a risk model with two classes of claims ⋮ Hawkes processes in insurance: risk model, application to empirical data and optimal investment ⋮ Risk theory of the second and third kind ⋮ Optimal reinsurance via BSDEs in a partially observable model with jump clusters ⋮ Lundberg inequalities in a diffusion environment ⋮ Ruin by dynamic contagion claims ⋮ The time to ruin for a class of Markov additive risk process with two-sided jumps ⋮ Optimal reinsurance-investment strategy for a dynamic contagion claim model ⋮ Regime-Switching Periodic Models For Claim Counts ⋮ Two-sided Lundberg inequalities in a Markovian environment

Cites Work

• Unnamed Item
• An introduction to the theory of point processes
• A CONVEXITY PROPERTY OF POSITIVE MATRICES
• A property of the generalized inverse Gaussian distribution with some applications
• Entropy, a useful concept in risk theory
• Exponential inequalities for ruin probabilities in the Cox case
• Martingales and insurance risk

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