Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD96 - 05/06/2011
Bonforte, M.; Grillo, G.; Vazquez, J.L.
Behaviour near extinction for the Fast Diffusion Equation on bounded domains | Abstract | | We consider the Fast Diffusion Equation posed in a bounded smooth domain with homogeneous Dirichlet
conditions. It is known that for in a certain range of the parameter m appearing in the equation all bounded positive solutions of such problem extinguish in a finite time, and also that such solutions approach a separate variable solution. Here, we are interested in describing the behaviour of the solutions near the extinction time. We first show that the convergence takes place uniformly in the relative error norm. Then, we study the question of rates of convergence. For m close to 1 we get such rates by means of entropy methods and weighted Poincarè inequalities. The analysis of the latter point makes an essential use of fine properties of a associated stationary elliptic problem, which has an independent interest. |
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QDD97 - 05/06/2011
Grillo, G.; Kovarik, H.; Pinchover, Y.
Sharp two-sided heat kernel estimates of twisted tubes and applications | Abstract | | We prove sharp on-diagonal bounds for the heat kernel of the Dirichlet Laplacian in locally twisted three-dimensional tubes. Such bounds show that any, suitably regular, local twisting speeds up the decay of the heat kernel with respect to the case of straight (untwisted) tubes. Moreover, the above large time decay is valid for a wide class of subcritical operators defined on a straight tube.
We also discuss some applications of this result, such as Sobolev inequalities and spectral estimates for Schroedinger operators.
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QDD93 - 04/11/2011
de Falco, C.; Porro, M.; Sacco, R.; Verri, M.
Multiscale Modeling and Simulation of Organic Solar Cells | Abstract | | In this article, we continue our mathematical study of organic photovoltaic device models started off in a previous work, focusing on the issue of accurately modeling the impact of the interface morphology on device performance.
To this end, we propose a multi-dimensional model
for bilayer organic solar cell devices with
arbitrary interface geometries derived by averaging the mass balance equations across the interface thickness. This yields a system of incompletely parabolic nonlinear PDEs to describe mass transport in the materials, coupled with ODEs localized at the heterojunction. We perform the numerical approximation of the differential system in stationary conditions and we apply it to the simulation of a variety of devices with different morphologies. |
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QDD92 - 03/29/2011
Bramanti, M.; Zhu, M.
L^{p} and Schauder estimates for nonvariational operators structured on Hörmander vector fields with drift | Abstract | | We consider linear second order nonvariational partial differential operators of the kind a_{ij}X_{i}X_{j}+X_{0}, on a bounded domain of R^{n}, where the X_{i} s (i=0,1,2,...,q, n>q+1) are real smooth vector fields satisfying Hörmander s condition and a_{ij} (i,j=1,2,...,q) are real valued, bounded measurable functions, such that the matrix {a_{ij}} is symmetric and uniformly positive. We prove that if the coefficients a_{ij} are Hölder continuous with respect to the distance induced by the vector fields, then local Schauder estimates on X_{i}X_{j}u, X_{0}u hold; if the coefficients belong to the space VMO with respect to the distance induced by the vector fields, then local L^{p} estimates on X_{i}_{j}u, X_{0}u hold. The main novelty of the result is the presence of the drift term X_{0}, so that our class of operators covers, for instance, Kolmogorov-Fokker-Planck operators. |
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QDD91 - 03/25/2011
Barucci, E.; Cosso, A.
Portfolio choices and VaR constraint with a defaultable asset | Abstract | | Assuming a Constant Elasticity of Variance (CEV) model for the asset price, that is a defaultable asset showing the so called leverage effect (high volatility when the asset price is low), a VaR constraint reevaluated over time induces an agent more risk averse than a logarithmic utility to take more risk than in the unconstrained setting. |
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QDD90 - 03/22/2011
Barucci, E.; Cosso, A.
Does an equity holding tax help to stabilize a VaR regulated financial market? | Abstract | | We investigate the capability of an equity holding tax to stabilize a VaR regulated financial market. We show that a VaR constraint induces high volatility in a distressed
financial market, the phenomenon is not observed in a market with risk averse unregulated traders. A tax on equity holding smoothes the peak of volatility and stabilizes the market at the cost of a generalized higher volatility. |
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QDD89 - 03/15/2011
Barucci, E.; Marazzina, D.
Optimal Investment, Stochastic Labor Income and Retirement | Abstract | | We address the optimal consumption-investment-retirement problem considering stochastic labor income. We study the Merton problem assuming that the agent has to take four different decisions: the retirement date which is irreversible; the labor and the consumption rate and the portfolio decision before retirement. After retirement the agent only chooses the portfolio and the consumption rate. We confirm some classical results and we show that labor, portfolio and retirement decisions interact in a complex way depending on the spanning opportunities. |
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QDD88 - 02/04/2011
Corsaro, S.; Marazzina, D.; Marino, Z.
Wavelet techniques for option pricing on advanced architectures | Abstract | | This work focuses on the development of a parallel pricing algorithm for Asian options based on the Discrete Wavelet Transform. Following the approach proposed in Fusai, et al. (2009), the pricing process requires the solution of a set of independent Fredholm integral equations of the second kind. Within this evaluation framework, our aim is to develop a robust parallel pricing algorithm based on wavelet techniques for the pricing problem of discrete monitoring arithmetic Asian options. In particular, the Discrete Wavelet Transform is applied in order to approximate the kernels of the integral equations. We discuss both the accuracy of the method and its scalability properties. |
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