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On the Probability of (Non-) Ruin in Infinite Time
Scandinavian Actuarial Journal, 2001In the context of the classical Poisson ruin model Gerber (1988a,b) and Shiu (1987, 1989) have obtained two formulae for the ruin and non ruin probabilities in infinite time. Here these two formulae are generalized to the case of an arbitrary premium process when all claims are integer-valued, as in Picard & Lefevre (1997).
Picard, P., Lefèvre, Claude
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Mixed poisson processes and the probability of ruin
Insurance: Mathematics and Economics, 1984zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seal, Hilary L., Gerber, Hans U.
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Ruin Probability in Models with Stochastic Premiums
Moscow University Mathematics Bulletin, 2020The paper focuses on the the ruin probability of an insurance company. Some generalizations of the classical Cramér-Lundberg model are considered; in particular, either the aggregate claims process or the aggregate premium process is not Poisson -- as commonly hypothesized in literature -- but constructed using a renewal process. Within this framework,
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Scandinavian Actuarial Journal, 1998
Abstract Upper and lower bounds are obtained for ruin probabilities with safety margin ρ in the case of known expectation, variance and range for the claim severity function.
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Abstract Upper and lower bounds are obtained for ruin probabilities with safety margin ρ in the case of known expectation, variance and range for the claim severity function.
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A Bound on the Probability of Ruin in Merton’s Model
Computational Mathematics and Modeling, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Morozov, V. V., Babin, V. A.
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On the Asymptotics of the Ruin Probability
Theory of Probability & Its Applications, 2015We obtain an asymptotic representation of the ruin probability for a random walk with negative drift when the upper bound of the strip tends to infinity. The result is expressed via distributions of the trajectory supremum and overshoot below negative level.
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The stability of the probability of ruin
Stochastic Models, 2019This article provides a computational formula for the the stability of the probability of ruin of the compound Poisson risk process.
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Ruin probability and local ruin probability in the random multi-delayed renewal risk model
Statistics & Probability Letters, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, Qingwu, Wang, Yuebao
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Estimation of ruin probabilities
Insurance: Mathematics and Economics, 1977Consider the compound Poisson claim size process generated by a distribution function B. Denote by W(t. x) the finite time non-ruin probability that the company will not be ruined before 1 starting with initial reserve x. Under appropriate conditions on B it is shown that W(t, χ)−W(∞, χ) is basically of the form exp{−θt−υχ}⋯t 32⋯χ for large t, where θ ...
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Ruin Probability for a Portfolio Including Options
Journal of Mathematical Sciences, 2002The author studies a standard \((B,S)\)-market consisting of a risk-free bond, growing exponentially at a fixed rate \(r\), and a stock, having initial value \(s_0\) and evolving stochastically to a value \(s_T\) at expiration date \(T\). At time \(0\), an investor sells different types of call and put options (based on the stock, with strike prices ...
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