A Study of Option Pricing Models – Lognormal or Hyperbolic Levy ? By Chen Chen This paper is an investigation into two option pricing models: widely-used Black-Scholes model and one of its augmented extensions – hyperbolic Levy model. Firstly, we have a detailed discussion about the celebrated Black-Scholes model. However, clearly there are many deficiencies in Black-Scholes assumptions. In ord...

Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are d...

In the early 60’s J. B. Keller and D. Levy discovered a fundamental property: instability tongues in Mathieu-type equations lose sharpness with addition of higher-frequency harmonics Mathieu potentials. Twenty years later, V. Arnold similar phenomenon on circle maps (and rediscovered result Levy). this paper we find third class object where type behavior takes place: area-preserving cylinder. l...

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anom...

In this paper, we study the extinction time of logistic branching processes which are perturbed by an independent random environment driven a Brownian motion. Our arguments use Lamperti-type representation is interesting on its own right and provides one to correspondence between latter family Feller diffusions spectrally positive Levy process. When perturbation (of diffusion) subordinator then...

We prove theorems of Landau and Hardy-Littlewood type for Goldbach, Chen, Lemoime-Levy and other binary partitions of positive integers. We also pose some new conjectures.

Optimization is a broad field for researchers to develop new algorithms solving various types of problems. There are popular techniques being worked on improvement. Grey wolf optimization (GWO) one such algorithm because it efficient, simple use, and easy implement. However, GWO has several drawbacks as stuck in local optima, low convergence rate, poor exploration. Several attempts have been ma...