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On the Ruin Problem of Collective Risk Theory [PDF]
The Annals of Mathematical Statistics, 1961 0. Summary. The theory of collective risk deals with an insurance business, for which, during a time interval (0, t) (1) the total claim X(t) has a compound Poisson distribution, and (2) the gross risk premium received is Xt. The risk reserve Z(t) = u + Xt - X(t), with the initial value Z(O) = u, is a temporally homogeneous Markov process.
N. U. Prabhu
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Weak limits of random coefficient autoregressive processes and their application in ruin theory [PDF]
Insurance: Mathematics and Economics, Elsevier, 2020, 91, pp.1-11, 2019 We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability and the discounted penalty function
Y. Dong, J Spielmann
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Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances [PDF]
Dependence Modeling, 2016 The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products.
Devolder Pierre, Lebègue Adrien
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Some stable algorithms in ruin theory and their applications. [PDF]
Insurance: Mathematics and Economics, 1996 AbstractIn this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin.
D Dickson
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Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process [PDF]
The Scientific World Journal, 2015 We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps.
Chuancun Yin, Kam Chuen Yuen, Ying Shen
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On the depletion problem for an insurance risk process: new non-ruin quantities in collective risk theory [PDF]
, 2015 The field of risk theory has traditionally focused on ruin-related quantities. In particular, the socalled Expected Discounted Penalty Function has been the object of a thorough study over the years.
Zied Ben-Salah +3 more
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Uniform Markov renewal theory and ruin probabilities in Markov random walks [PDF]
, 2004 Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that {(X_n,S_n),n\geq0} is
Cheng–Der Fuh
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Error estimates for De Vylder type approximations in ruin theory [PDF]
arXiv, 2017 Due to its practical use, De Vylder's approximation of the ruin probability has been one of the most popular approximations in ruin theory and its application to insurance. Surprisingly, only heuristic and numerical evidence has supported it, to some extent.
Azmi Makhlouf
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Ruin theory with excess of loss reinsurance and reinstatements [PDF]
Applied Mathematics and Computation, 2011 Abstract The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer–Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin
Hansjörg Albrecher, Sandra Haas
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Properties of a Risk Measure Derived from Ruin Theory [PDF]
The Geneva Risk and Insurance Review, 2010 This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level.
Julien Trufin +2 more
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