On the time to ruin for Erlang(2) risk processes.
From MaRDI portal
Publication:1413289
DOI10.1016/S0167-6687(01)00091-9zbMath1074.91549OpenAlexW2021047139MaRDI QIDQ1413289
David C. M. Dickson, Christian Hipp
Publication date: 16 November 2003
Published in: Insurance Mathematics \& Economics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0167-6687(01)00091-9
Related Items
SOME EXTENSIONS OF THE RESIDUAL LIFETIME AND ITS CONNECTION TO THE CUMULATIVE RESIDUAL ENTROPY ⋮ Analysis of some ruin-related quantities in a Markov-modulated risk model ⋮ Periodic threshold-type dividend strategy in the compound Poisson risk model ⋮ The perturbed compound Poisson risk model with two-sided jumps ⋮ Optimal investment and premium control for insurers with ambiguity ⋮ On the expectation of total discounted operating costs up to default and its applications ⋮ Perturbed MAP Risk Models with Dividend Barrier Strategies ⋮ The expected discounted penalty function in the generalized Erlang\((n)\) risk model with two-sided jumps and a constant dividend barrier ⋮ The moments of the time to ruin in dependent Sparre Andersen models with Coxian claim sizes ⋮ Lévy insurance risk process with Poissonian taxation ⋮ On a ruin model with both interclaim times and premiums depending on claim sizes ⋮ On a renewal risk process with dependence under a Farlie–Gumbel–Morgenstern copula ⋮ On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes ⋮ Discrete time ruin probability with Parisian delay ⋮ Expected discounted penalty function and asymptotic dependence of the severity of ruin and surplus prior to ruin for two-sided Lévy risk processes ⋮ Gerber-Shiu function for a class of Markov-modulated Lévy risk processes with two-sided jumps ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ Joint moments of discounted claims and discounted perturbation until ruin in the compound Poisson risk model with diffusion ⋮ The two-barrier escape problem for compound renewal processes with two-sided jumps ⋮ Asymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes ⋮ The expected discounted penalty function for a kind of time-correlated risk model based on the renewal argument in consideration of the by-claim ⋮ Optimal Parisian-type dividend payments penalized by the number of claims for the classical and perturbed classical risk process ⋮ Potential measures and expected present value of operating costs until ruin in renewal risk models with general interclaim times ⋮ On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy ⋮ On the Gerber–Shiu function with random discount rate ⋮ On a general class of renewal risk process: analysis of the Gerber-Shiu function ⋮ On Erlang(2) Risk Process Perturbed by Diffusion ⋮ Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process ⋮ “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 ⋮ “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 ⋮ “Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003 ⋮ The Time Value of Ruin in a Sparre Andersen Model ⋮ The density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claims ⋮ On the severity of ruin in a Markov-modulated risk model ⋮ Dividend Payments in a Risk Model Perturbed by Diffusion with Multiple Thresholds ⋮ Approximations for the Gerber-Shiu expected discounted penalty function in the compound poisson risk model ⋮ The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model ⋮ Extension of the past lifetime and its connection to the cumulative entropy ⋮ The distribution and asympotic behaviour of the negative Wiener–Hopf factor for Lévy processes with rational positive jumps ⋮ The perturbed compound Poisson risk model with multi-layer dividend strategy ⋮ The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion ⋮ The Moments of the Time of Ruin in Markovian Risk Models ⋮ Analysis of ruin measures for the classical compound Poisson risk model with dependence ⋮ A Risk Model Based on Markov Chains with Marked Transitions ⋮ A Risk Model with Delayed Claims ⋮ Unnamed Item ⋮ On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(\(n\)) interclaim times ⋮ A generalized penalty function for a class of discrete renewal processes ⋮ A unifying approach to the analysis of business with random gains ⋮ Erlang risk models and finite time ruin problems ⋮ Ruin time and aggregate claim amount up to ruin time for the perturbed risk process ⋮ On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process ⋮ Randomized observation periods for the compound Poisson risk model: the discounted penalty function ⋮ The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model ⋮ On a risk model with dependence between interclaim arrivals and claim sizes ⋮ On a class of discrete time renewal risk models ⋮ Distributions of the surplus before ruin, the deficit at ruin and the claim causing ruin in a class of discrete time risk models ⋮ Finite time non-ruin probability for Erlang claim inter-arrivals and continuous inter-dependent claim amounts ⋮ On the Joint Distributions of the Time to Ruin, the Surplus Prior to Ruin, and the Deficit at Ruin in the Classical Risk Model ⋮ Analysis of a Generalized Penalty Function in a Semi-Markovian Risk Model ⋮ On the evaluation of expected penalties at claim instants that cause ruin in the classical risk model ⋮ The Markov additive risk process under an Erlangized dividend barrier strategy ⋮ On a Gerber-Shiu type function and its applications in a dual semi-Markovian risk model ⋮ Markov-dependent risk model with multi-layer dividend strategy ⋮ On the discounted distribution functions for the Erlang(2) risk process ⋮ On the expected discounted penalty functions for two classes of risk processes under a threshold dividend strategy ⋮ On a perturbed Sparre Andersen risk model with multi-layer dividend strategy ⋮ On the improved thinning risk model under a periodic dividend barrier strategy ⋮ The Gerber-Shiu penalty functions for two classes of renewal risk processes ⋮ Dividend barrier strategy: proceed with caution ⋮ On a generalized Gerber-Shiu function in a compound Poisson model perturbed by diffusion ⋮ Ruin and dividend measures in the renewal dual risk model ⋮ Expected discounted penalty function of Erlang(2) risk model with constant interest ⋮ The Gerber-Shiu discounted penalty functions for a risk model with two classes of claims ⋮ Moments of the time of ruin, surplus before ruin and the deficit at ruin in the Erlang(N) risk process ⋮ An operator property of the distribution of a nonhomogeneous Poisson process with applications ⋮ On properties of continuous-time random walks with non-Poissonian jump-times ⋮ Differential equations for ruin probability in a special risk model with FGM copula for the claim size and the inter-claim time ⋮ On the dual risk model with diffusion under a mixed dividend strategy ⋮ Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times ⋮ A class of Sparre Andersen risk process ⋮ On a risk model with random incomes and dependence between claim sizes and claim intervals ⋮ On a Sparre Andersen risk model with time-dependent claim sizes and jump-diffusion perturbation ⋮ On a perturbed MAP risk model under a threshold dividend strategy ⋮ Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang ⋮ On a perturbed compound Poisson risk model under a periodic threshold-type dividend strategy ⋮ On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps ⋮ The Gerber-Shiu discounted penalty function in the classical risk model with impulsive dividend policy ⋮ On the expected discounted penalty function for the compound Poisson risk model with delayed claims ⋮ Gerber-Shiu functionals for classical risk processes perturbed by an \(\alpha\)-stable motion ⋮ On the analysis of ruin-related quantities in the delayed renewal risk model ⋮ The expected discounted penalty function under a renewal risk model with stochastic income ⋮ The Gerber-Shiu discounted penalty function in the stationary renewal risk model. ⋮ The maximum surplus distribution before ruin in an Erlang(\(n\)) risk process perturbed by diffusion ⋮ The discounted penalty function with multi-layer dividend strategy in the phase-type risk model ⋮ A note on discounted compound renewal sums under dependency ⋮ The distributions of the time to reach a given level and the duration of negative surplus in the Erlang(2) risk model ⋮ The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. ⋮ On the Gerber-Shiu discounted penalty function in a risk model with delayed claims ⋮ A note on a Lévy insurance risk model under periodic dividend decisions ⋮ The Gerber-Shiu discounted penalty function of sparre Andersen risk model with a constant dividend barrier ⋮ A unified analysis of claim costs up to ruin in a Markovian arrival risk model ⋮ The compound Poisson risk model with dependence under a multi-layer dividend strategy ⋮ On the joint distributions of surplus immediately before ruin and the deficit at ruin for Erlang(2) risk processes. ⋮ A perturbed risk model with dependence between premium rates and claim sizes ⋮ Analysis of the Gerber-Shiu function and dividend barrier problems for a risk process with two classes of claims ⋮ Finite time ruin problems for the Erlang\((2)\) risk model ⋮ An algebraic operator approach to the analysis of Gerber-Shiu functions ⋮ An elementary approach to discrete models of dividend strategies ⋮ Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models ⋮ On a perturbed by diffusion compound Poisson risk model with delayed claims and multi-layer dividend strategy ⋮ Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy ⋮ On the ruin problem in a Markov-modulated risk model ⋮ On a class of stochastic models with two-sided jumps ⋮ Asymptotic correlation structure of discounted incurred but not reported claims under fractional Poisson arrival process ⋮ Constant dividend barrier in a risk model with interclaim-dependent claim sizes ⋮ Discounted aggregate claim costs until ruin in the discrete-time renewal risk model ⋮ The compound Poisson risk model under a mixed dividend strategy ⋮ Laplace transform of the survival probability under Sparre Andersen model ⋮ On the expected discounted penalty function in a delayed-claims risk model ⋮ On a nonparametric estimator for the finite time survival probability with zero initial surplus ⋮ A generalized penalty function in the Sparre Andersen risk model with two-sided jumps ⋮ A matrix operator approach to a risk model with two classes of claims ⋮ Number of claims and ruin time for a refracted risk process ⋮ The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times ⋮ On a risk model with stochastic premiums income and dependence between income and loss ⋮ A class of delayed renewal risk processes with a threshold dividend strategy ⋮ On a class of renewal risk models with a constant dividend barrier ⋮ On the expected discounted penalty functions for two classes of risk processes ⋮ On a compound Poisson risk model with delayed claims and random incomes ⋮ On ruin for the Erlang \((n)\) risk process ⋮ An application of fractional differential equations to risk theory ⋮ The expected discounted penalty at ruin in the Erlang (2) risk process ⋮ A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium ⋮ The compound Poisson risk model with a threshold dividend strategy ⋮ On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution ⋮ The compound Poisson risk model with multiple thresholds ⋮ Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times ⋮ On a generalization from ruin to default in a Lévy insurance risk model ⋮ On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times ⋮ A connection between the discounted and non-discounted expected penalty functions in the Sparre Andersen risk model ⋮ On corrected phase-type approximations of the time value of ruin with heavy tails ⋮ On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula ⋮ Maximum surplus and \(R_n\) class of distributions with an application to dividends ⋮ On the probability of ruin in the compound Poisson risk model with potentially delayed claims ⋮ Estimating the Gerber-Shiu function in a compound Poisson risk model with stochastic premium income ⋮ Risk model with fuzzy random individual claim amount ⋮ The Markovian regime-switching risk model with a threshold dividend strategy ⋮ Ultimate ruin probability in the Sparre Andersen model with dependent claim sizes and claim occurrence times ⋮ On the renewal risk model under a threshold strategy ⋮ An uncertain alternating renewal insurance risk model ⋮ The expected discounted penalty function under a risk model with stochastic income ⋮ Escape probabilities from an interval for compound Poisson processes with drift ⋮ Joint moments of the total discounted gains and losses in the renewal risk model with two-sided jumps ⋮ A modified insurance risk process with uncertainty ⋮ The expected discounted penalty function for two classes of risk processes perturbed by diffusion with multiple thresholds ⋮ A ruin model with compound Poisson income and dependence between claim sizes and claim intervals ⋮ Gerber-Shiu analysis of a risk model with capital injections ⋮ On the discounted penalty function in a Markov-dependent risk model ⋮ Gerber-Shiu analysis with two-sided acceptable levels
Cites Work
- Unnamed Item
- Ruin probabilities for Erlang (2) risk processes
- On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
- The moments of the time of ruin, the surplus before ruin, and the deficit at ruin
- Analysis of a defective renewal equation arising in ruin theory
- Ruin Problems for Phase-Type(2) Risk Processes
- Exact solutions for ruin probability in the presence of an absorbing upper barrier
- A laplace transform representation in a class of renewal queueing and risk processes
- On the Time Value of Ruin