Pricing of asian-type and basket options via bounds

© 2017 Society for Industrial and Applied Mathematics. This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket, and options on the volume-weighted average price. The use of lower and upper bounds is proposed in response to the inherent difficulty in finding analytical representations for the true price of these options and the requirement for numerical procedures to be fast and efficient. We demonstrate that in some cases lower bounds allow for the dimensionality of the problem to be reduced and that these methods provide reasonable approximations to the price of the option

New analytic models of traversable wormholes

The analytic solution of the general relativity equations for spherically symmetric wormholes are given. We investigate the special case of a "traversable" wormhole i.e., one allowing the signal to pass through it. The energy-momentum tensor of wormhole matter is represented as a superposition of a spherically symmetric magnetic field and dust matter with negative matter density. The dynamics of the model are investigated. We discuss both the solution of the equation with a Lambda-term and without it. Superposing enough dust matter, a magnetic field, and a Lambda-term can produce a static solution, which turns out to be a spherical Multiverse model with an infinite number of wormholes connected spherical universes. Corresponding solution can be static and dynamic.Comment: 15 pages, 2 figure

Automated Calculation of Thermal Rate Coefficients using Ring Polymer Molecular Dynamics and Machine-Learning Interatomic Potentials with Active Learning

We propose a methodology for fully automated calculation of thermal rate coefficients of gas phase chemical reactions, which is based on combining the ring polymer molecular dynamics (RPMD) with the machine-learning interatomic potentials actively learning on-the-fly. Based on the original computational procedure implemented in the RPMDrate code, our methodology gradually and automatically constructs the potential energy surfaces (PESs) from scratch with the data set points being selected and accumulated during the RPMDrate simulation. Such an approach ensures that our final machine-learning model provides reliable description of the PES which avoids artifacts during exploration of the phase space by RPMD trajectories. We tested our methodology on two representative thermally activated chemical reactions studied recently by RPMDrate at temperatures within the interval of 300--1000~K. The corresponding PESs were generated by fitting to only a few thousands automatically generated structures (less than 5000) while the RPMD rate coefficients retained the deviation from the reference values within the typical convergence error of RPMDrate. In future, we plan to apply our methodology to chemical reactions which proceed via complex-formation thus providing a completely general tool for calculating RPMD thermal rate coefficients for any polyatomic gas phase chemical reaction

Symbolic representation and classification of integrable systems

This is a review paper of recent results in the perturbative symmetry approach in the symbolic representation