DSpace Community:
http://hdl.handle.net/2440/299
2017-03-25T11:38:20ZClassification of the automorphism and isometry groups of Higgs bundle moduli spaces
http://hdl.handle.net/2440/103953
Title: Classification of the automorphism and isometry groups of Higgs bundle moduli spaces
Author: Baraglia, D.
Abstract: Let Mn,d be the moduli space of semi-stable rank n, trace-free Higgs bundles with fixed determinant of degree d on a Riemann surface of genus at least 3. We determine the following automorphism groups of Mn,d: (i) the group of automorphisms as a complex analytic variety, (ii) the group of holomorphic symplectomorphisms, (iii) the group of Kähler isomorphisms, (iv) the group of hypercomplex automorphisms, (v) the group ofhyper-Kähler isomorphisms. When n and d are coprime we show that Mn,d admits an anti-holomorphic isomorphism if and only if the corresponding Riemann surface admits such a map. We then use this to determine the isometry group of Mn,d.2016-01-01T00:00:00ZPricing options in a Markov regime switching model with a random acceleration for the volatility
http://hdl.handle.net/2440/103832
Title: Pricing options in a Markov regime switching model with a random acceleration for the volatility
Author: Elliott, R.J.; Chan, L.; Siu, T.K.
Abstract: This article discusses option pricing in a Markov regime-switching model with a random acceleration for the volatility. A key feature of the model is that the volatility of the underlying risky security is randomly accelerated by a coefficient which is modulated by a continuous-time, finite-state Markov chain. Consequently, the degree of acceleration in volatility depends on the state of an economy represented by the state of the chain. A system of coupled partial differential equations for the prices of a standard European option over different economic states is derived. Using the homotopy analysis method originating from algebraic topology, a pricing formula for a standard European option is derived in the form of an infinite series. In addition, we give convergence conditions and compute implied volatilities using Monte-Carlo simulations. The implied volatilities can capture some important empirical features such as the implied volatility skew and smile for both VIX options and stock index options. We also provide numerical comparisons between call option prices from the first-order approximation of the proposed numerical method to those from the Monte-Carlo simulations.2016-01-01T00:00:00ZHyperbolic neighbourhoods as organizers of finite-time exponential stretching
http://hdl.handle.net/2440/103780
Title: Hyperbolic neighbourhoods as organizers of finite-time exponential stretching
Author: Balasuriya, S.; Kalampattel, R.; Ouellette, N.T.
Abstract: Hyperbolic points and their unsteady generalization – hyperbolic trajectories – drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. In infinite-time steady or periodic flows, the stable and unstable manifolds attached to each hyperbolic trajectory mark fluid elements that asymptote either towards or away from the hyperbolic trajectory, and which will therefore eventually experience exponential stretching. But typical experimental and observational velocity data are unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighbourhood, that marks the portion of the domain that is instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and empirical verification from model and experimental data, that the hyperbolic neighbourhoods profoundly impact the Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighbourhoods is directly correlated to larger finite-time Lyapunov exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighbourhoods have a geometrical structure that is ‘regular’ in a specific sense.2016-01-01T00:00:00ZVariation of Hodge structure for generalized complex manifolds
http://hdl.handle.net/2440/103670
Title: Variation of Hodge structure for generalized complex manifolds
Author: Baraglia, D.
Abstract: Abstract not available2014-01-01T00:00:00Z