Financial Modelling with Jump Processes

By René L. Schilling. 2005

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In Economics and Econometrics

Citations in the corpus

Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “Many applications of GH distributions, their subclasses, and related distributions are found in mathematical finance (Schoutens, 2003; Cont and Tankov, 2004; Barndorff-Nielsen and Halgreen, 1990; Madan et al., 1998; Barndorff-Nielsen, 1998; Barndorff-Nielsen and Prause, 2001; Carr et al., 2002) and…”
A concave—convex elliptic problem involving the fractional Laplacian (2010, background): “The proof follows and standard argument that can be found, for instance in [21, 40].”
Fractional Diffusion Models of Option Prices in Markets With Jumps (2007, background): “The literature proposes a number of ways of choosing an EMM under which pricing of instruments is performed.”
Nonparametric Estimation for Lévy Models Based on Discrete-Sampling (2009, neutral): “[11] and [30]).”
Compound random measures and their use in Bayesian non‐parametrics (2014, background): “(The representation of a CRM should also take into account a deterministic component; see Cont and Tankov (2004). This consideration also applies later when we shall talk about vectors of CRMs.”
Obstacle problems for integro-differential operators: Higher regularity of free boundaries (2019, background): “Namely, they arise when considering optimal stopping problems for Lévy processes with jumps, which have been used in pricing models for American options since the 1970s; see [9,26].”
Lévy Processes—From Probability to Finance and Quantum Groups (2004, background): “Readers who want to learn more about “Lévy finance” should consult [12], [4] , chapter 5 of [1], and references therein.”
A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian (2016, background): “In the last few years, the nonlocal operators have taken relevance because they arise in a number of applications in many fields, for instance, game theory, finance, image processing, Lévy processes, and optimization, see [7, 9, 16, 3, 14] and the references therein.”
Estimation of the characteristics of a Lévy process observed at arbitrary frequency (2010, neutral): “[6], Chapter 4.”
Consistency of general bootstrap methods for degenerate U-type and V-type statistics (2009, background): “(3.1) Cont and Tankov [14] describe a NIG process as a subordinated Brownianmotionwith drift ϑ ∈ R, volatility σ > 0 andwith an inverse Gaussian process with variance κ at time 1 as subordinator.”
Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations (2015, background): “Among these, we mention obstacle problems [10], finance [16], quasi-geostrophic flows [11, 15], anomalous diffusion [27, 37, 39].”
A critical fractional equation with concave-convex power nonlinearities (2013, background): “For more details and applications, see [8, 11, 25, 34, 59, 60] and the references therein.”
Nonparametric estimation for L\'evy processes from low-frequency observations (2007, methodology): “Cont and Tankov (2004). This formula indicates that estimating νσ is strongly related to estimating φ in a C2-sense.”
Characterization of dependence of multidimensional Lévy processes using Lévy copulas (2006, background): “[3] discusses examples of multidimensional models with jumps, which are constructed with the help of Lévy copulas.”
Counterparty Risk and Funding: A Tale of Two Puzzles (2014, methodology): “The main references are Cont and Tankov (2004), Ikeda and Watanabe (1989), Protter (2004), Kunita (2010) and Crépey (2013).”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, background): “The rigorous study of such nonlinear models has been delayed until this time by the mathematical difficulties in treating at the same time the nonlinearity and fractional diffusion.”