Discounted probabilities and ruin theory in the compound binomial model
type: Item
instance of: scholarly article
title: Discounted probabilities and ruin theory in the compound binomial model
zbMATH Open document ID: 1013.91063
DOI: 10.1016/S0167-6687(99)00053-0
author: Shixue Cheng
author: H. U. Gerber
author: E. S. W. Shiu
published in: Insurance Mathematics \& Economics
publication date: 2001-02-18T00:00:00Z
review text: A discrete-time model is considered. The aggregate claims are modeled as a compound binomial process. The possible claim amounts are integral multiples of the annual premium. The main goal of the paper is to study the function \(f(x,y;u)\), which is the ``discounted'' probability of ruin, given an initial surplus of \(u\), such that the surplus just before ruin is \(x\), and the deficit \(dt\) ruin is \(y\). Applications include an explicit expression for the expected discounted value of a payment 1 at the time of ruin and formulas for the expected time of ruin.
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1525145
zbMATH Keywords: risk theory
zbMATH Keywords: ruin probability
zbMATH Keywords: compound binomial model
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
cites work: Classical numerical ruin probabilities
cites work: On the distribution of the surplus prior to ruin
cites work: Q5538132
cites work: Q5624436
cites work: The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin
cites work: On the Time Value of Ruin
cites work: Pricing Perpetual Options for Jump Processes
cites work: From ruin theory to pricing reset guarantees and perpetual put options
cites work: Q4481936
cites work: The moments of ruin time in the classical risk model with discrete claim size distribution
cites work: Ruin probabilities in the compound binomial model
full work available at URL: s0167-6687(99)00053-0
OpenAlex ID: W2059784050
description: scientific article; zbMATH DE number 1525145