Exit problems for spectrally negative Levy processes and applications to (Canadized) Russian options

By Florin Avram, Andreas E. Kyprianou, Martijn Pistorius. 2004

279 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a44a1264a9b0223ae5d9065fc3aa77ca4ca2450e

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Citations in the corpus

On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum (2004, methodology): “From the study of [ 2 ] and Section 3.2, it appears that the Laplace transforms of the exit times of X and Y from nite and semi-nite intervals can be expressed in terms of W (q) and Z(q), where Z(q)(x) = 1 +q R x 0 W (q)(y)dy and W (q) is the scale function of a spectrally”
An Excursion-Theoretical Approach to Some Boundary Crossing Problems and the Skorokhod Embedding for Reflected Lévy Processes (2007, methodology): “the proof of Theorem 1 in [2]).”
The McKean stochastic game driven by a spectrally negative Lévy process (2008, background): “Firstly, as was already found in numerous papers concerning optimal stopping problems driven by spectrally one sided Lévy processes (cf. Alili and Kyprianou (2005), Chan (2004) and Avram et al. (2004)), smooth pasting breaks down when the Lévy process is of bounded variation.”
Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem (2008, unknown): “[1]), thus e + a ∧τ − 0 va(Xt∧τ+ a ∧τ− 0 ) is a Px-martingale for each x ∈ (0, a).”
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes (2007, methodology): “By means of straightforward calculations based on solving the corresponding boundaryvalue problem (see also [2], [3], and [19]) it follows that when α = 1/θ < 0 holds, we have”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, methodology): “…finance and queueing theory and so on one 3 faces the consideration of the fluctuation theory for a class of spectrally negative Lévy processes; For example, The exit problems have recently been used by Avram et al. (2004) in the context of finance in connection with American and Canadian options.”
On the optimal dividend problem for a spectrally negative Lévy process (2007, background): “In [4] it was shown that the function Z(q) of X is given by Z(x) = n+1 ∑”
Perpetual options and Canadization through fluctuation theory (2003, unknown): “The interested reader is refered to [1].”
De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, background): “The following was established in [6] (Theorem 1 and Remark 4): for q, r ≥ 0, we have Ex [ e b+rUb σb ] =e + (q − ψ(r)) ∫ x”
General tax Structures and the Lévy Insurance Risk Model (2009, unknown): “By a classical application of the compensation formula (see, for example, the treatment of a related problem in [4]) we have, for z > 0, y ∈ [0, a), and q ≥ 0, E(e−qςa ; a − Yςa− ∈ dy, Yςa − a ∈ dz) = E [∑ t≥0 exp{−q(L−1 t− + ρa(εt ))} 1{sups<t εs≤a,ρa(εt )<σ(εt ), a−εt (ρa−)∈dy, εt (ρa)−a∈dz} ]”
Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering (2007, background): “…and Kyprianou and Pistorius (2003) for some representations (though not explicit calculations) based on the Wiener–Hopf factorization related to the overshoot problems for general Lévy processes; and see also Avram et al. (2004) and Rogers (2000) for first passage times with one-sided jumps.”
On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, background): “[2]), and the optimal dividend models with “reflecting barriers” (e.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “The following theorem is a compilation of results taken from [9] and [82].”