Fluctuation Theory for Lévy Processes

By R. Doney. 2007

196 citations recorded by the source corpus.

Subfields: Management Information Systems, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96110b98b88dac4169a9a1e13b36d29b17aa7fa0

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In Management Information Systems

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Citations in the corpus

Valuing equity-linked death benefits in jump diffusion models (2013, background): “The title of Dufresne and Gerber (1991b), “Risk theory for the compound Poisson process that is perturbed by diffusion,” is indicative of the actuarial perception of the jump diffusion model. In finance, the jump diffusion model is considered from a substantially different perspective. The economic ”
Suprema of Lévy processes (2011, background): “For more account on the fluctuation theory we refer the reader to [5, 13, 31].”
Special, conjugate and complete scale functions for spectrally negative Lévy processes (2007, background): “It is in this context of ruin theory that they make their earliest appearance in the works of [64], [61] and then later either explicitly or implicitly in the work of [24] and [36, 37], [60] and [53], the real value of scale functions as a class with which one may express a whole range of fluctuatio”
On the Lamperti stable processes (2008, background): “The second class corresponds to that of stable processes conditioned to stay positive (see for instance [9, 11]), denoted by (X,Px).”
Some explicit identities associated with positive self-similar Markov processes. (2007, unknown): “3) in [15]).”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “It well known that (see Bertion (1996), Kyprianou (2006) and Doney (2007)) u(q)(x, y) =W (q)(x)e−Φ(q)y −W (q)(x− y).”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “Behaviour at zero: For all cases we observe W (0) = 0 in Figure 1 and W (0) = 0 in Figure 2, in agreement with formula (23).”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “These results are very important from the theoretical point of view; for example, they can be used to prove general theorems about short/long time behavior (see [7, 18, 21] and [29]).”