On the Density and Moments of the Time of Ruin with Exponential Claims
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Publication:4661670
DOI10.2143/AST.33.1.1036zbMath1062.60007OpenAlexW4232571841MaRDI QIDQ4661670
Gordon E. Willmot, Steve Drekic
Publication date: 30 March 2005
Published in: ASTIN Bulletin (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2143/ast.33.1.1036
Laplace transformBessel functioncompound geometric tailGauss hypergeometric seriesGerber-Shiu equationruin probabiltiy
Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05)
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APPROXIMATING THE DENSITY OF THE TIME TO RUIN VIA FOURIER-COSINE SERIES EXPANSION ⋮ A surplus process involving a compound Poisson counting process and applications ⋮ Nonparametric estimation of the finite time ruin probability in the classical risk model ⋮ Integro-local theorems in boundary crossing problems for compound renewal processes ⋮ Decomposition of default probability under a structural credit risk model with jumps ⋮ Boundary crossing problems for compound renewal processes ⋮ On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps ⋮ Moments of the ruin time in a Lévy risk model ⋮ Asymptotics for the moments of the time to ruin for the compound Poisson model perturbed by diffusion ⋮ Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions ⋮ Symbolic calculation of the moments of the time of ruin. ⋮ Finite time ruin problems for the Erlang\((2)\) risk model ⋮ On the ruin time distribution for a Sparre Andersen process with exponential claim sizes ⋮ Approximations in the problem of level crossing by a compound renewal process ⋮ Adaptive control strategies and dependence of finite time ruin on the premium loading ⋮ On the Moments of the Time of Ruin with Applications to Phase-Type Claims ⋮ On the Gerber-Shiu discounted penalty function for subexponential claims ⋮ On a nonparametric estimator for the finite time survival probability with zero initial surplus ⋮ The expected discounted penalty function: from infinite time to finite time ⋮ The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims ⋮ The Moments of the Time of Ruin in Markovian Risk Models ⋮ Erlangian approximation to finite time ruin probabilities in perturbed risk models ⋮ Erlang risk models and finite time ruin problems ⋮ Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims ⋮ On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model ⋮ “On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model,” David Landriault and Gordon Willmot, Volume 13, No. 2, 2009 ⋮ Gerber-Shiu analysis of a risk model with capital injections ⋮ Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes
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