On the Ruin Problem of Collective Risk Theory
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Publication:3286759
DOI10.1214/AOMS/1177704970zbMath0103.13302OpenAlexW2058280335MaRDI QIDQ3286759
Publication date: 1961
Published in: The Annals of Mathematical Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aoms/1177704970
Related Items (38)
Finite-time ruin probabilities using bivariate Laguerre series ⋮ A note on some joint distribution functions involving the time of ruin ⋮ A remark on survival probabilities for a weighted poisson process ⋮ Approximations to ruin probability in the presence of an upper absorbing barrier ⋮ Probability modelling across the continents ⋮ The joint distribution of the Parisian ruin time and the number of claims until Parisian ruin in the classical risk model ⋮ On the accuracy of phase-type approximations of heavy-tailed risk models ⋮ The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin ⋮ Moment and polynomial bounds for ruin-related quantities in risk theory ⋮ Nonparametric estimation of the finite-time survival probability with zero initial capital in the classical risk model ⋮ Optimal lower barrier on modified surplus process ⋮ Some ruin problems for the MAP risk model ⋮ Formula for the supremum distribution of a spectrally positive \(\alpha \)-stable Lévy process ⋮ The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model ⋮ Gerber-Shiu analysis in the compound Poisson model with constant inter-observation times ⋮ A delayed dual risk model ⋮ Distributional study of finite-time ruin related problems for the classical risk model ⋮ On the Time Value of Ruin ⋮ The probability of ruin in a discrete semi-Markov risk model ⋮ On the distribution of classic and some exotic ruin times ⋮ The expected discounted penalty function: from infinite time to finite time ⋮ An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes ⋮ On finite-time ruin probabilities for classical risk models ⋮ Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis ⋮ Recursive approximating to the finite-time Gerber-Shiu function in Lévy risk models under periodic observation ⋮ A multidimensional ruin problem and an associated notion of duality ⋮ Optimal Dynamic Reinsurance ⋮ The moments of ruin time in the classical risk model with discrete claim size distribution ⋮ Monotone Stochastic Recursions and their Duals ⋮ A Note on Negative Customers, GI/G/1 Workload, and Risk Processes ⋮ Stochastic clearing systems ⋮ On the interaction between risk and queueing theories ⋮ Inequality extensions of Prabhu's formula in ruin theory ⋮ Erlang risk models and finite time ruin problems ⋮ Conjugate processes and the simulation of ruin problems ⋮ Approximations for the probability of ruin within finite time ⋮ The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t) ⋮ Gerber-Shiu analysis of a risk model with capital injections
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