A Special Study of the Mixed Weighted Fractional Brownian Motion

Khalaf, Anas D.; Zeb, Anwar; Saeed, Tareq; Abouagwa, Mahmoud; Djilali, Salih; Alshehri, Hashim M.

doi:10.3390/fractalfract5040192

Cited by 8 publications

(4 citation statements)

References 29 publications

(42 reference statements)

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“…In what follows, we present certain attributes of the mixed weighted-fBm through the proposition delineated hereafter. For more detailed information about the properties of the mixed weighted-fBm, one can refer to [18,26].…”

Section: Mixed Weighted-fbmmentioning

confidence: 99%

“…This research also adopts such an approach, constructing a mixture of standard Brownian motion and weighted-fBm as a linear combination. Khalaf et al [18] pointed out that this mixture, along with the asymptotic stationary properties for weighted-fBm, opened up the possibility of the mixture being a martingale or equivalent to Brownian motion, as it is the same as mfBm. This indicates that the pricing model of the underlying asset driven by a mixed weighted fractional Brownian motion is arbitrage-free.…”

Section: Introductionmentioning

confidence: 99%

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Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

Xu,

Yang

2023

Fractal Fract

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This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment. We construct a pricing model for European options driven by fuzzy mixed weighted fractional Brownian motion with jumps. By converting the partial differential equation (PDE) into a Cauchy problem, we derive explicit solutions for both European call options and European put options. The figures and tables demonstrating the effectiveness of the results highlight the suitability of the fuzzy mixed weighted fractional Brownian motion with jump model for option pricing.

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Section: Mixed Weighted-fbmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

Xu,

Yang

2023

Fractal Fract

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“…for all t, v ≥ 0. Note that, when H = 1 2 , S H corresponds to the well known Brownian motion B. Sub-fractional Brownian motion has properties that are similar to those of fractional Brownian motion, such as the following: long-range dependence, Self-similarity, Hölder pathes, and it satisfies [17][18][19][20][21][22][23].…”

Section: Preliminariesmentioning

confidence: 99%

Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

Khalaf

Saeed

Abu-Shanab

et al. 2022

Entropy

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This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by dxt=θ(μ−xt)dt+dStH, with θ>0, μ∈R being unknown and t≥0; here, SH represents a sub-fractional Brownian motion (sfBm). We introduce new estimators θ^ for θ and μ^ for μ based on discrete time observations and use techniques from Nordin–Peccati analysis. For the proposed estimators θ^ and μ^, strong consistency and the asymptotic normality were established by employing the properties of SH. Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H.

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“…For k = 1, the GFCP and the GCP reduce to the time fractional Poisson process (TFPP) (see [3]) and the Poisson process, respectively. For other recently introduced fractional stochastic processes, we refer the reader to Khalaf et al [4,5].…”

Section: Introductionmentioning

confidence: 99%

Some Compound Fractional Poisson Processes

Khandakar

Kataria

2022

Fractal Fract

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In this paper, we introduce and study fractional versions of the Bell–Touchard process, the Poisson-logarithmic process and the generalized Pólya–Aeppli process. The state probabilities of these compound fractional Poisson processes solve a system of fractional differential equations that involves the Caputo fractional derivative of order 0<β<1. It is shown that these processes are limiting cases of a recently introduced process, namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property, etc., for these processes. Further, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes.

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A Special Study of the Mixed Weighted Fractional Brownian Motion

Cited by 8 publications

References 29 publications

Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps

Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

Some Compound Fractional Poisson Processes

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