Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 866 prodotti
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QDD177 - 22/04/2014
Baccarin, S.; Marazzina, D.
Passive Portfolio Management over a Finite Horizon with a Target Liquidation Value under Transaction Costs and Solvency Constraints | Abstract | | We consider a passive investor who divides his capital between two assets: a risk-free money market instrument and an index fund, or ETF, tracking a broad market index. We model the evolution of the market index by a lognormal diffusion. The agent faces both fixed and proportional transaction costs and solvency constraints. The objective is to maximize the expected utility from the portfolio liquidation at a fixed horizon but if the portfolio reaches a pre-set target value then the position in the risky asset is liquidated. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We show the existence of an impulse policy which is arbitrarily close to the optimal one by reducing the model to a sequence of iterated optimal stopping problems. The value function and the quasi-optimal policy are computed numerically by an iterative finite element discretization technique. We present extended numerical results in the case of a CRRA utility function, showing the non-stationary shape of the optimal strategy and how it varies with respect to the model parameters. The numerical experiments reveal that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times. |
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QDD176 - 21/04/2014
Grillo, G.; Muratori, M.; Punzo, F.
On the Asymptotic Behaviour of Solutions to the Fractional Porous Medium Equation with Variable Density | Abstract | | We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable density. We prove that if the density decays slowly at infi nity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at in finity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation. |
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QDD175 - 20/02/2014
Maddalena, F.; Percivale, D.; Tomarelli, F.
Adhesion of Soft Nonlinear Elastic Membranes | Abstract | | We study a variational model describing the adhesion of a soft nonlinear membrane to an elastic-breakable membrane. We provide a description of the conditions characterizing debonding and global collapse of the structure. Some consequences of the general results are explicitated in the case of ring-shaped geometry. |
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QDD174 - 11/02/2014
Bacchelli, V.; Pierotti, D.
Identification problem for a hyperbolic equation with Robin condition | Abstract | | We discuss an identification problem for the one dimensional wave equation with the Robin condition on an unknown part of the boundary. We prove that it is possible to identify both the unknown boundary and the Robin coefficient by two pairs of additional measurements. |
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QDD172 - 31/01/2014
Grillo, G.; Muratori, M.; Punzo, F.
Weigthed fractional porous media equations: exixtende and uniqueness of weak solution with measure data | Abstract | | We shall prove existence and uniqueness of solutions to a class of porous media equations driven by weighted fractional Laplacians when the initial data are positive finite measures on the Euclidean space R^d . In particular, Barenblatt-type solutions exist and are unique for the evolutions considered. The weight can be singular at the origin, and must have a sufficiently slow decay at infinity (power-like). Such kind of evolutions seems to have not been treated before even as concerns their linear, non-fractional analogues.
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QDD173 - 31/01/2014
Al-Gwaiz, M.; Benci, V.; Gazzola, F.
Bending and stretching energies in a rectangular plate modeling suspension bridges | Abstract | | A rectangular plate modeling the roadway of a suspension bridge is considered. Both the contributions of the bending and stretching energies are analyzed. The latter plays an important role due to the presence of the free edges. A
linear model is first considered; in this case, separation of variables is used to determine explicitly the deformation of the plate in terms of the vertical load. Moreover, the same method allows us to study the spectrum of the linear operator and the least eigenvalue. Then the stretching energy is
introduced without linearization and the equation becomes quasilinear; the nonlinear term also affects the boundary conditions. We consider two quasilinear models; the surface increment model (SIM) in which the stretching energy is proportional to the increment of surface and a nonlocal model (NLM) introduced by Berger in the 50 s. The (SIM) and the (NLM) are studied in detail. According to the strength of prestressing we prove the existence of multiple equilibrium positions. |
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QDD171 - 20/01/2014
Berchio, E.; Gazzola, F.
Torsional instability in a fish-bone model for suspension bridges | Abstract | | We consider a mathematical model for the study of the dynamical behavior of suspension bridges. We show that internal resonances, which depend on the bridge structure
only, are the origin of torsional instability. We obtain both theoretical and numerical estimates of the thresholds of instability. Our method is based on a finite dimensional projection of the phase space which reduces the stability analysis of the model to the stability of suitable nonlinear Hill equations.
This gives an answer to a long-standing question about the origin of torsional instability. |
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QDD170 - 17/01/2014
Arioli, G.
Insegnare Matematica con Mathematica | Abstract | | In questo articolo vogliamo discutere le possibilità offerte da software di calcolo simbolico, in particolare parliamo di Mathematica, nell’insegnamento della Matematica nelle scuole primarie e secondarie. Dopo un breve excursus sulla ricerca recente in didattica della matematica e sull’importanza del problem solving nell’insegnamento della matematica, illustriamo come Mathematica possa essere un ottimo strumento didattico, e introduciamo tre applet create con Mathematica per illustrare le possibilità di questo strumento. |
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