On a partial integrodifferential equation of Seal's type

DOI10.1016/j.insmatheco.2015.03.004zbMath1318.91124OpenAlexW2009976580MaRDI QIDQ2347058

Gordon E. Willmot

Publication date: 26 May 2015

Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.insmatheco.2015.03.004

zbMATH Keywords

finite-time ruin probabilitydeficit at ruintime of ruinmixed Erlang distributionLundberg's fundamental equationLagrange's implicit function theorem

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Integro-partial differential equations (35R09)

Related Items (9)

Finite-time ruin probabilities using bivariate Laguerre series ⋮ A note on some joint distribution functions involving the time of ruin ⋮ A multinomial approximation approach for the finite time survival probability under the Markov-modulated risk model ⋮ Distributional study of finite-time ruin related problems for the classical risk model ⋮ On the distribution of classic and some exotic ruin times ⋮ The expected discounted penalty function: from infinite time to finite time ⋮ A Fourier-cosine method for finite-time ruin probabilities ⋮ Recursive approximating to the finite-time Gerber-Shiu function in Lévy risk models under periodic observation ⋮ Gerber-Shiu analysis of a risk model with capital injections

Cites Work

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• The joint distribution of the time to ruin and the number of claims until ruin in the classical risk model
• On Queues with Poisson Arrivals
• The numerical calculation ofU(w, t), the probability of non-ruin in an interval (0,t)
• The Density of the Time to Ruin in the Classical Poisson Risk Model
• On the Time Value of Ruin
• A Combinatorial Method in the Theory of Queues
• Loss Models

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