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A Fourier-cosine method for finite-time ruin probabilities
Insurance, Mathematics & Economics, 2021In this paper, we study the finite-time ruin probability in the risk model driven by a Levy subordinator, by incorporating the popular Fourier-cosine method. Our interest is to propose a general approximation for any specified precision provided that the
Wing Yan Lee +4 more
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Minimizing ruin probability under the Sparre Anderson model
Communications in Statistics - Theory and Methods, 2021In this paper, we consider the problem of minimizing the ruin probability of an insurance company in which the surplus process follows the Sparre Andersen model.
Linlin Tian, Lihua Bai
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Salvaging Ruins: Reverting Blind Retinas into Functional Visual Sensors
2014Blindness is one of the most devastating conditions affecting the quality of life. Hereditary degenerative diseases, such as retinitis pigmentosa, are characterized by the progressive loss of photoreceptors, leading to complete blindness. No treatment is known, the current state-of-the-art of restoring vision are implanted electrode arrays.
Marion, Mutter +2 more
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Insurance, Mathematics & Economics, 2020
In this paper, we study the optimal dividend and capital injection problem with the penalty payment at ruin. The dividend strategy is assumed to be restricted to a small class of absolutely continuous strategies with bounded dividend density.
Ran Xu, J. Woo
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In this paper, we study the optimal dividend and capital injection problem with the penalty payment at ruin. The dividend strategy is assumed to be restricted to a small class of absolutely continuous strategies with bounded dividend density.
Ran Xu, J. Woo
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A Functional Approach for Ruin Probabilities
Stochastic Models, 2006In the classical risk model with Poisson arrivals, we study a functional approach which can be used to obtain new approximation formulae for the probability of ultimate ruin. In particular, we consider a map Φ between appropriate function spaces with Φ(f) = ψ, where f denotes the density of claim sizes in the model and ψ is the function that gives the ...
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On series expansions for scale functions and other ruin-related quantities
Scandinavian Actuarial Journal, 2019In this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Levy processes.
David Landriault, Gordon E. Willmot
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Scale Functions and Ruin Probabilities
2013The two main results from the previous chapters concerning the law of the maximum and minimum of the Cramer–Lundberg process can now be put to use in order to establish our first results concerning the classical ruin problem. We introduce the so-called scale functions, which will prove to be indispensable, both in this chapter and later, when ...
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Assessing Function and the Ruin Category
2018This chapter addresses objections that could be raised against the claims I make in Chap. 5. One could argue that industrial or urban ruins are not “real” ruins, because they seem to exhibit markedly different properties from structures like the ruins of antiquity, and because they simply have not been around long enough to earn the designation.
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Numerical solution for ruin probability of continuous time model based on neural network algorithm
Neurocomputing, 2019In the classical risk model, the ruin probability satisfies the renewal Integro-differential equation, which only has an analytic solution when the claim distribution obeys the exponential distribution.
Tao Zhou +3 more
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On a function-theoretic ruin problem
2007Let \(X\) be a random variable with values in \(N_0\) and let \[ \varphi(z)= \sum^\infty_{k= 0} P\,(X= k) z^k= \sum^\infty_{k= 0} a_k z^k \] be its generating function. Then \(a_j\geq 0\) for all \(j\), \(\varphi(1)= 1\), and it is assumed \(a_0> 0\). Let \(m\in N\) and \(S_0\) another random variable with values in \(N_0\).
Jensen, Gerd, Pommerenke, Christian
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