Stochastic Integration with Jumps

By K. Bichteler. 2002

195 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/1555e920891bca0d423e3b5afdf640ea6b92b858

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Citations in the corpus

About the Pricing Equations in Finance (2011, methodology): “Any square integrable martingale or martingale measure is an L2-integrator in the sense of Bichteler [13] (see Theorem 2.”
Ornstein–Uhlenbeck Processes and Extensions (2009, methodology): “Corresponding exactly to the decomposition in (8) is the Lévy-Ito representation of the process as a shift vector plus Brownian plus “small jump” plus “large jump” components:”
Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit (2019, background): “If, for each θ , b and σ in (7) are Lipschitz-continuous in x uniformly in t ∈ [0 , 1] , then there exists a mapping f θ : W → W , such that X = f θ ( W ) , and this mapping is progressively measurable [Bichteler, 2002, Sec.”
Fluctuations of Lévy Processes with Applications (2014, background): “of Bichteler (2002) for a detailed description of what this means.”
Existence, Uniqueness and Regularity of Parabolic SPDEs Driven by Poisson Random Measure (2005, background): “[7] K. Bichteler.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “what is to be understood by a spectrally negative L´evy process. Suppose that (W;F;F;P) is a ﬁltered probability space with ﬁltration F=fF t :t 0gwhich is naturally enlarged (cf. Deﬁnition 1.3.38 of [17]). A L´evy process on this space is a strong Markov, F-adapted process X =fX t :t 0g with cadl` a”
The numéraire portfolio in semimartingale financial models (2007, background): “Under this assumption, there exists a sequence of [0,1]-valued predictable processes (hn)n∈N such that each πn := hnρ is X-integrable up to T and the sequence of terminal values ((πn · X)T )n∈N is unbounded in probability (readers unfamiliar with this fact should consult [5], Corollary 3.”
Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison (2008, unknown): “We refer the reader to the literature [1, 25, 29] regarding the definition of the integral process of P̃-measurable integrands with respect to random measures such as μ(dt, de), its compensator dt⊗ ζdρ := ζt(ω, e)ρ(de)dt or its compensatrix (compensated measure) μ̃(dt, de) = μ(dt, de)− ζt(ω, e)ρ(de)”
The McKean stochastic game driven by a spectrally negative Lévy process (2008, background): “Using the fact that XL−1t = t we find for ε small enough 0 ≤ 1 ε P(Aε) = 1 ε E [ ∫ ε∧L∞ 0 dt · 1{ǫθ<θ+ε ∀θ<t}ϕ(t) ] (24) ≤ 1 ε ∫ ε 0 dt · n(ǫ(ρt+ε) > −c) ≤ 1 ε ∫ 2ε 0 dt · n(ǫ(ρt) > −c).”