Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica. La presenza del fulltext è lacunosa per i prodotti antecedenti maggio 2006.
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QDD144  15/01/2013
Baccarin, S.; Marazzina, D.
Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints  Abstract   We investigate a portfolio optimization problem for an agent who invests in two assets, a riskfree and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected utility
from the portfolio liquidation at a terminal finite horizon. 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 quasivariational inequality. We compute numerically the optimal
policy by a an iterative finite element discretization technique, presenting extended numerical results in the case of a constant relative risk aversion utility function. Our results show that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buyandhold trading strategy where the agent recalibrates his portfolio very few times. This contrasts sharply with the continuous interventions of the Merton s model without transaction costs. 

QDD143  11/01/2013
Gazzola, F.
Hexagonal design for stiffening trusses  Abstract   We consider the problem of choosing the best design for stiffening trusses of plates, such as bridges. We suggest to cover the plate with regular hexagons which fit side to side. We show that this design has some important advantages when compared with alternative designs. 

QDD142  30/11/2012
Terracini, S.; Verzini, G.; Zilio, A.
Uniform Holder bounds for strongly competing systems involving the square root of the laplacian  Abstract   For a class of competitiondiffusion nonlinear systems involving the square root of the Laplacian, including the fractional GrossPitaevskii system, we prove that uniform boundedness implies Holder boundedness for every exponent less than 1/2, uniformly as the interspecific competition parameter diverges. Moreover we prove that the limiting profile is Holder continuous of exponent 1/2. This system arises, for instance, in the relativistic HartreeFock approximation theory for mixtures of BoseEinstein condensates in different hyperfine states. 

QDD141  15/11/2012
Hartshorne, R.; Lella, P.; Schlesinger, E:
Smooth curves specialize to extremal curves  Abstract   Let H_{d,g} denote the Hilbert scheme of locally CohenMacaulay curves of degree d and genus g in projective three space. We show that, given a smooth irreducible curve C of degree d and genus g, there is a rational curve {[C_t]} in H_{d,g} such that C_t for t neq 0 is projectively equivalent to C, while the special fibre C_0 is an extremal curve. It follows that smooth curves lie in a unique connected component of H_{d,g}. We also determine necessary and sufficient conditions for a locally CohenMacaulay curve to admit such a specialization to an extremal curve. 

QDD138  12/11/2012
Baccarin, S; Marazzina, D.
Optimal impulse control of a portfolio with a fixed transaction cost  Abstract   The aim of this work is to investigate a portfolio optimization problem in presence of fixed transaction costs. We consider an economy with two assets, one risky and one riskfree, and an agent fully described by its power utility function. We show how fixed transaction costs influence the agent s behavior, showing when it is optimal to recalibrate his/her portfolio, paying the transaction costs. 

QDD139  12/11/2012
Berchio, E.; Ferrero, A.; Grillo, G.
Stability and qualitative properties of radial solutions of the LaneEmdenFowler equation on Riemannian models  Abstract   We study existence, uniqueness and stability of radial solutions of the LaneEmdenFowler equation  Delta_g u=u^{p1}u in a class of Riemannian models (M,g) of dimension n>2 which includes the classical hyperbolic space H^n as well as manifolds with sectional curvatures unbounded below. Sign properties and asymptotic behavior of solutions are influenced by the critical Sobolev exponent while the socalled JosephLundgren exponent is involved in the stability of solutions. 

QDD140  12/11/2012
Berchio, E.
A family of HardyRellich type inequalities involving the L^2norm of the Hessian matrices  Abstract   We derive a family of HardyRellich type inequalities in H^2( Omega) cap H_0^1( Omega) involving the scalar product between Hessian matrices. The constants found are optimal and the existence of a boundary remainder term is discussed. 

QDD137  30/10/2012
Grillo, G.; Kovarik, H.
Weighted dispersive estimates for twodimensional Schroedinger operators with AharonovBohm magnetic field  Abstract   We consider twodimensional Schroedinger operators with AharonovBohm magnetic field and an additional electric potential.
We obtain an explicit leading term of the asymptotic expansion of the unitary group associated to H for large times in weighted L^2 spaces. In particular, we show that the magnetic field improves the decay of the unitary group with respect to the unitary group generated by nonmagnetic Schroedinger operators, and that the decay rate in time is determined by the magnetic flux. 
