Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.Comment: 17 page

Numerical methods for pricing and hedging american options

164 σ.Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες στην Οικονομία”Αντικέιμενο της παρούσας εργασίας είναι η παρουσίαση αριθμητικών μεθόδων για την τιμολόγηση αμερικάνικων δικαιωμάτων. Πιο συγκεκριμένα έγινε χρήση της μεθόδου των πεπερασμένων στοιχείων και της μεθόδου των πεπερασμένων διαφορών. Το γραμμικό σύστημα που προκύπτει από τις ανωτέρω μεθόδους επιλύθηκε με χρήση της επαναληπτικής μεθόδου PSOR. Επιπροσθέτως για την τιμολόγηση αμερικάνικων δικαιωμάτων με δύο υποκείμενα προϊόντα, μετασχηματίσαμε την 2D Black Scoles στη γενικευμένη εξίσωση διαχύσης. Για την αντιμετώπιση τυχών διαταραχών που προκύπτουν στην εξίσωση διαχύσης εισάγαμε την Streamline Upwind Galerkin μέθοδο. Τέλος με χρήση των πεπερασμένων διαφορών έγινε διακριτοποίηση των Greeks Delta, Gamma, Theta.American options allow the holder to exercise the option early prior to expiry. Therefore, the evaluation of these option is more complicated than the European options, since we have to determine not only the option value, but also the time that should be exercised. Thus numerical methods should n\be applied to deal with the pricing of these option. In this thesis we introduced the finite elements, finite differences and binomial method.Moreover, we discritized the american put option worst of two assets using finite element method by transforming the 2D Black Scholes to the 2D general diffusion equation. Due to the fact that spurious oscilations may occur we introduced the Streamline Upwind Galerkin method. Finally, we presented some Greeks: Delta, Gamma and Theta using finite differences.Νικόλας Σ. Καρπαθόπουλο

Wheeler–DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries. © 2016, The Author(s)

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization. © 2018, Springer Science+Business Media, LLC, part of Springer Nature

Interference correlations between like pions in the reaction K-p→K-pπ+π+π-π- at 8.25 GeV/c

We have observed correlations in the transverse momentum of pion pairs with like and unlike charge produced in 8.25 GeV/c K-p→K-pπ+π+π-π- interaction. We found that a Bose-Einstein interference effect accounts partially for these correlations. Evidence is presented indicating that the correlations observed in the above reaction can be described by the reflections from the occurence of physical resonances. © 1983 Springer-Verlag