Fractional Skellam processes with applications to finance

DOI10.2478/s13540-014-0184-2zbMath1310.60034OpenAlexW2012836475MaRDI QIDQ2939445

Alexander Kerss, Alla Sikorskii, Nikolai N. Leonenko

Publication date: 22 January 2015

Published in: Fractional Calculus and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-014-0184-2

zbMATH Keywords

Mittag-Leffler distributionhigh frequency financial datafractional Poisson processfractional Skellam process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Fractional processes, including fractional Brownian motion (60G22) Probability distributions: general theory (60E05) Fractional derivatives and integrals (26A33)

Related Items (14)

Compositions of Poisson and Gamma processes ⋮ First passage times over stochastic boundaries for subdiffusive processes ⋮ Multivariate integer-valued time series with flexible autocovariances and their application to major hurricane counts ⋮ Queuing models with Mittag-Leffler inter-event times ⋮ Dynamic intersectoral models with power-law memory ⋮ Concept of dynamic memory in economics ⋮ Applications of Hilfer-Prabhakar operator to option pricing financial model ⋮ Modeling of financial processes with a space-time fractional diffusion equation of varying order ⋮ Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates ⋮ Fractional risk process in insurance ⋮ On the transient behaviour of fractional \(M/M/\infty\) queues ⋮ On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators ⋮ Series representation of the pricing formula for the European option driven by space-time fractional diffusion ⋮ Skellam and time-changed variants of the generalized fractional counting process

Cites Work

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• The fractional Poisson process and the inverse stable subordinator
• Mittag-Leffler functions and their applications
• Stochastic solutions for fractional wave equations
• A fractional generalization of the Poisson processes
• Beyond the Poisson renewal process: a tutorial survey
• Triangular array limits for continuous time random walks
• Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes
• Parameter estimation for fractional Poisson processes
• Fractional Poisson processes and related planar random motions
• Fractional Poisson process
• On Mittag-Leffler-type functions in fractional evolution processes
• Infinite divisibility of random variables and their integer parts
• Large deviations for fractional Poisson processes
• Fractional Cauchy problems on bounded domains
• Some limit theorems for Hawkes processes and application to financial statistics
• Integer-valued Lévy processes and low latency financial econometrics
• Fractal Activity Time Models for Risky Asset with Dependence and Generalized Hyperbolic Distributions
• Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion
• SEMI-STATIC HEDGING OF BARRIER OPTIONS UNDER POISSON JUMPS
• FRACTIONAL PROCESSES: FROM POISSON TO BRANCHING ONE
• Trading volume in models of financial derivatives
• On the convergence of quadratic variation for compound fractional Poisson processes
• Fractional Discrete Processes: Compound and Mixed Poisson Representations
• Limit theorems for occupation times of Markov processes
• Student processes
• Modelling microstructure noise with mutually exciting point processes
• The Frequency Distribution of the Difference between Two Independent Variates following the same Poisson Distribution
• The Frequency Distribution of the Difference Between Two Poisson Variates Belonging to Different Populations
• Stochastic models for fractional calculus

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