Related papers: Financial rogue waves
Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow…
An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in…
Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…
The efforts to understand the physics of rogue waves have motivated the study of mechanisms that produce rare, extreme events, often through analogous optical setups. As many studies have reported nonlinear generation mechanisms, recent…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…
Powerful rogue ocean waves have been objects of fascination for centuries. Elusive and awe-inspiring, with the ability to inflict catastrophic damage, rogue waves remain unpredictable and imperfectly understood. To gain further insight into…
The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…
Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…
We advance a statistical theory of extreme event emergence in random nonlinear wave systems with self-similar intermediate asymptotics. We show, within the framework of a generic (1 + 1)D nonlinear Schrodinger equation with linear gain,…
In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…
We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…
In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrodinger equation (NLSE) extended by R.…
The spectra of rogue waves of Manakov equations that exist in both focusing or defocusing regimes are derived in analytic form. These spectra are asymmetric during their whole expansion-contraction cycle. They have triangular shape at each…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…
We show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center.…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…
We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…
Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this…
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…