Ruin probabilities and decompositions for general perturbed risk processes

By Miljenko Huzak, Mihael Perman, Hrvoje Sikic, Zoran Vondraček. 2004

99 citations recorded by the source corpus.

We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, and the perturba- tion being a spectrally negative Levy process with zero expectation. We derive a Pollaczek-Hinchin type formula for the survival proba- bility of that risk process, and give an interpretation of the formula based on the decomposition of the dual risk process at modified ladder epochs.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7876c242a7e40770d98dfb40ae14804617ea7747

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Citations in the corpus

General tax Structures and the Lévy Insurance Risk Model (2009, background): “Introduction and main results Recent advances in the analysis of the ubiquitous ruin problem from the theory of insurance risk has seen a tendency to replace the classical Cramér–Lundberg surplus process with a general spectrally negative Lévy process; see, for example, [2], [10], [11], and [21], to”
Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem (2008, background): “of literature concerning actuarial mathematics which explores the interaction of classical models of risk and fine properties of Lévy processes with a view to gaining new results on both sides (see for example [2, 10, 18, 19, 23, 22, 24, 26, 28, 31]).”
Refracted Lévy processes (2008, unknown): “See, for example, [2] [7] [12] [13] [17] [18] [20] [26] [30].”
Occupation Times of Refracted Lévy Processes (2012, unknown): “See for example [1,4–6,8, 9,12,17,18].”
WIENER-HOPF FACTORIZATION FOR LEVY PROCESSES HAVING POSITIVE JUMPS WITH RATIONAL TRANSFORMS (2008, background): “Among other works that study different aspects of ruin probabilities for Lévy processes, we mention [15], where asymptotic results for overshoots were obtained, [11], where a convolution formula was obtained for a classical claim process perturbed by an α-stable Lévy process, and [13], where a Polla”
Distribution of the Present Value of Dividend Payments in a Lévy Risk Model (2007, unknown): “[9], and Garrido and Morales [7].”
An Optimal Dividends Problem with a Terminal Value for Spectrally Negative Lévy Processes with a Completely Monotone Jump Density (2009, unknown): “[1], [3], [8], [9], [11], [14], [16], [19], [20], and [23]).”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “…mathematics, the first passage problem is very important to the ruin problems; see, for example, among others, Yang and Zhang (2001), Klüppelberg et al. (2004), Huzak et al. (2004a, 2004b), Zhou (2005), Garrido and Morales (2006), Biffis and Kyprianou (2010) and Billis and Morales (2010).”
Fluctuations of spectrally negative Markov additive processes (2008, background): “(14) Note also that F(β)− qI is always invertible for β < Φ(q).”
A Lévy Insurance Risk Process with Tax (2008, unknown): “[6], [8], [9], [11], [13], and [18].”
On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes (2008, unknown): “Explanations for why this particular process serves as an appropriate generalization of the classical compound Poisson risk process can be found in, for example, [13, 18, 23].”
Ruin probabilities and overshoots for general Lévy insurance risk processes (2004, methodology): “The main concern in [26] is to analyze the supremum and ladder height processes of X , Z and C.”
Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, background): “Keywords: Reflected Lévy process; passage problem; integrated exponential Lévy process; insurance risk process; ruin 2000 Mathematics Subject Classification: Primary 60K05; 60K15; 91B30 Secondary 60G70; 60J55”
On The Expected Discounted Penalty function for Lévy Risk Processes (2006, methodology): “Huzak et al. (2004) work with the general model (1) and give a general ladder–height decomposition of the ruin probability.”