The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion.

DOI10.1016/S0167-6687(03)00143-4zbMath1055.91042OpenAlexW1998798886MaRDI QIDQ1413337

S. N. Chiu, Chuan-Cun Yin

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(03)00143-4

zbMATH Keywords

Ruin probabilityDeficit at ruinTime of ruinSurplus processRenewal equationSurplus prior to ruin

Mathematics Subject Classification ID

Related Items (31)

\(\mathrm{G}/\mathrm{M}/1\) type structure of a risk model with general claim sizes in a Markovian environment ⋮ A note on the perturbed compound Poisson risk model with a threshold dividend strategy ⋮ The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy ⋮ Optimal investment and premium control for insurers with ambiguity ⋮ The Gerber-Shiu function for the compound Poisson Omega model with a three-step premium rate ⋮ Ruin probabilities for the phase-type dual model perturbed by diffusion ⋮ Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion ⋮ Four approaches to compute the probability of ruin in the compound Poisson risk process with diffusion ⋮ On the ruin probabilities for a general perturbed renewal risk process ⋮ Nonparametric estimation of some dividend problems in the perturbed compound Poisson model ⋮ On the expected discounted penalty function for risk process with tax ⋮ On Ruin Probability for a Risk Process Perturbed by a Lévy Process with no Negative Jumps ⋮ Phase-type approximations perturbed by a heavy-tailed component for the Gerber-Shiu function of risk processes with two-sided jumps ⋮ On first and last ruin times of Gaussian processes ⋮ The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest ⋮ The perturbed Sparre Andersen model with a threshold dividend strategy ⋮ On a Classical Risk Model with a Constant Dividend Barrier ⋮ The use of vector-valued martingales in risk theory ⋮ Pricing the Zero-Coupon Bond and its Fair Premium Under a Structural Credit Risk Model with Jumps ⋮ A limit theorem for the time of ruin in a Gaussian ruin problem ⋮ A quintuple law for Markov additive processes with phase-type jumps ⋮ When does surplus reach a certain level before ruin? ⋮ The perturbed compound Poisson risk process with investment and debit interest ⋮ A generalised Gerber–Shiu measure for Markov-additive risk processes with phase-type claims and capital injections ⋮ On the ruin probability for the Cox correlated risk model perturbed by diffusion ⋮ The compound Poisson process perturbed by a diffusion with a threshold dividend strategy ⋮ The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion ⋮ Dividend payments in a perturbed compound Poisson model with stochastic investment and debit interest ⋮ The dividend function in the jump-diffusion dual model with barrier dividend strategy ⋮ Omega model for a jump-diffusion process with a two-step premium rate ⋮ The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Risk theory for the compound Poisson process that is perturbed by diffusion
• The surpluses immediately before and at ruin, and the amount of the claim causing ruin
• Aspects of risk theory
• On the discounted penalty at ruin in a jump-diffusion and the perpetual put option
• From ruin theory to pricing reset guarantees and perpetual put options
• Asymptotic estimates for the probability of ruin in a Poisson model with diffusion
• Ruin problems and dual events
• The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
• A generalized defective renewal equation for the surplus process perturbed by diffusion.
• 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
• Some distributions for classical risk process that is perturbed by diffusion
• On the Distribution of the Surplus Prior and at Ruin
• On the Time Value of Ruin

This page was built for publication: The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion.