262 research outputs found
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.Dupire equation, parameter identification, optimal control, optimality conditions, SQP method, primal-dual active set strategy
Efficient hedging in Bates model using high-order compact finite differences
We evaluate the hedging performance of the scheme developed in B. Düring, A. Pitkin, ”High-order compact finite difference scheme for option pricing in stochastic volatility jump models”, 2017. We compare the scheme’s hedging performance to standard finite difference methods in different examples. We observe that the new scheme achieves fourth-order convergence, outperforming a standard, second-order central finite difference approximation in all our experiments
Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments
Symmetry Induced 4-Wave Capillary Wave Turbulence
We report theoretical and experimental results on 4-wave capillary wave
turbulence. A system consisting of two inmiscible and incompressible fluids of
the same density can be written in a Hamiltonian way for the conjugated pair
. When given the symmetry , the set of weakly non-linear
interacting waves display a Kolmogorov-Zakharov (KZ) spectrum
in wave vector space. The wave system was studied experimentally with two
inmiscible fluids of almost equal densities (water and silicon oil) where the
capillary surface waves are excited by a low frequency random forcing. The
power spectral density (PSD) and probability density function (PDF) of the
local wave amplitude are studied. Both theoretical and experimental results are
in fairly good agreement with each other.Comment: 6 pages, 2 figure
Pre-oil globalization in a rural community: the Late Islamic village of Sahlat in the Suhar region
Archaeology of the Near Eas
Kinetic models for optimal control of wealth inequalities
We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker-Planck based models and taxation-redistribution policies and the present approach are also discussed
Fourier analysis of wave turbulence in a thin elastic plate
The spatio-temporal dynamics of the deformation of a vibrated plate is
measured by a high speed Fourier transform profilometry technique. The
space-time Fourier spectrum is analyzed. It displays a behavior consistent with
the premises of the Weak Turbulence theory. A isotropic continuous spectrum of
waves is excited with a non linear dispersion relation slightly shifted from
the linear dispersion relation. The spectral width of the dispersion relation
is also measured. The non linearity of this system is weak as expected from the
theory. Finite size effects are discussed. Despite a qualitative agreement with
the theory, a quantitative mismatch is observed which origin may be due to the
dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov
casade.Comment: accepted for publication in European Physical Journal B see
http://www.epj.or
Transient dynamics for sequence processing neural networks
An exact solution of the transient dynamics for a sequential associative
memory model is discussed through both the path-integral method and the
statistical neurodynamics. Although the path-integral method has the ability to
give an exact solution of the transient dynamics, only stationary properties
have been discussed for the sequential associative memory. We have succeeded in
deriving an exact macroscopic description of the transient dynamics by
analyzing the correlation of crosstalk noise. Surprisingly, the order parameter
equations of this exact solution are completely equivalent to those of the
statistical neurodynamics, which is an approximation theory that assumes
crosstalk noise to obey the Gaussian distribution. In order to examine our
theoretical findings, we numerically obtain cumulants of the crosstalk noise.
We verify that the third- and fourth-order cumulants are equal to zero, and
that the crosstalk noise is normally distributed even in the non-retrieval
case. We show that the results obtained by our theory agree with those obtained
by computer simulations. We have also found that the macroscopic unstable state
completely coincides with the separatrix.Comment: 21 pages, 4 figure
- …