fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Abstract. Option pricing models with a stochastic volatility are more realistic than the Black-Scholes model which uses a constant volatility. The prices of options based on such models can be obtained by solving a parabolic partial differential equation. Particularly, we consider the model presented by Heston. The variables in these problems are the time, the underlying asset value, and the vo...

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

We consider a recent successful model of leptons as Kerr-Newman type Black Holes in a Quantum Mechanical context. The model leads to a cosmology which predicts an ever expanding accelerating universe with decreasing density and to the conclusion that at Compton wavelength scales, electrons would exhibit low dimensionality, both of which conclusions have been verified by several independent expe...

XTE J1748-288 is a black hole X-ray transient which went into outburst in 1998 June. The X-ray lightcurves showed canonical morphologies, with minor variations on the “Fast Rise Exponential Decay” profile. The radio source, however, reached an unusually high flux density of over 600 mJy. This high radio flux was accompanied by an exceptional (> 20%) fractional linear polarisation, the variabili...

In this paper, we investigate option valuation problems under the fractional Black–Scholes model. The aim is to propose a pricing formula for the European option with transaction costs, where the costs structure contains fixed costs, a cost propositional to the volume traded, and a cost proportional to the value traded. Precisely, we provide an approximate solution of the nonlinear Hoggard–Whal...

We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and MuhleKarbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem....

Pricing American options using partial (integro-)differential equation based methods leads to linear complementarity problems (LCPs). The numerical solution of these problems resulting from the Black-Scholes model, Kou’s jumpdiffusion model, and Heston’s stochastic volatility model are considered. The finite difference discretization is described. The solutions of the discrete LCPs are approxim...

In this research work, our chief target is to elaborate an analytical solution of the fractional linear complement problem related evaluation American put option generated by Black and Scholes model using Adomian decomposition method, a numerical study set forward perform theoretical result. Compared existent we prove that result has prompt convergence solution.

The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including composite indices (Standard and Poor's 500...