1,721,018 research outputs found
Systemic risk governance in a dynamical model of a banking system with stochastic assets and liabilities
Full text linkWe consider the problem of governing systemic risk in an assets–liabilities dynamical model of a banking system. In the model considered, each bank is represented by its assets and liabilities. The net worth of a bank is the difference between its assets and liabilities and bank is solvent when its net worth is greater than or equal to zero; otherwise, the bank has failed. The banking system dynamics is defined by an initial value problem for a system of stochastic differential equations whose independent variable is time and whose dependent variables are the assets and liabilities of the banks. The banking system model presented generalizes those discussed in Fouque and Sun (in: Fouque, Langsam (eds) Handbook of systemic risk, Cambridge University Press, Cambridge, pp 444–452, 2013) and Fatone and Mariani (J Glob Optim 75(3):851–883, 2019) and describes a homogeneous population of banks. The main features of the model are a cooperation mechanism among banks and the possibility of the (direct) intervention of the monetary authority in the banking system dynamics. By “systemic risk” or “systemic event” in a bounded time interval, we mean that in that time interval at least a given fraction of banks have failed. The probability of systemic risk in a bounded time interval is evaluated via statistical simulation. Systemic risk governance aims to maintain the probability of systemic risk in a bounded time interval between two given thresholds. The monetary authority is responsible for systemic risk governance. The governance consists in the choice of assets and liabilities of a kind of “ideal bank” as functions of time and in the choice of the rules for the cooperation mechanism among banks. These rules are obtained by solving an optimal control problem for the pseudo mean field approximation of the banking system model. Governance induces banks in the system to behave like the “ideal bank”. Shocks acting on the banks’ assets or liabilities are simulated. Numerical examples of systemic risk governance in the presence and absence of shocks acting on the banking system are studied
Optimal solution of the liquidation problem under execution and price impact risks
Full text linkWe consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. As a consequence of his trading activity, during the execution of the liquidation order, the investor has no guarantees that the placed order is executed immediately; it may go unfilled, partially filled or filled in excess. The uncertainty in the execution affects the trading activity of the investor and the asset share price dynamics generating additional sources of noise: the execution risk and the price impact risk, respectively. Assuming the two sources of noise correlated and driven by the cumulative effect of the investor trading strategy, we study the problem of finding the optimal liquidation strategy adopted by the investor in order to maximize the expected revenue resulting from the liquidation. The mathematical model of the liquidation problem presented here extends the model of Almgren and Chriss [Optimal execution of portfolio transactions. J. Risk, 2000, 3(2), 5–39] to include execution and price impact risks. The liquidation problem is modeled as a linear quadratic stochastic optimal control problem with the finite horizon and, under some assumptions about the functional form for the magnitude of execution and price impact risks, is solved explicitly. The derived solution coincides with the optimal trading strategy obtained in the absence of execution uncertainty for an asset price with a modified growth rate. This suggests that the uncertainty in the execution modifies the directional view of the investor about the future growth rate of the asset price
Low-cost denoising and deblurring using a novel nonlinear diffusion technique
No full textAn algorithm for the treatment of images affected by both blurring and salt&pepper noise is
proposed with a cost only proportional to the number of pixels. The methodology uses an
ad-hoc discretization scheme for the Laplace operator, multiplied by a suitable nonlinear term
depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one
step of the procedure is in general needed, leading to significant time savings. The procedure
is successfully tested on some standard black&white images
High-order discretization of backward anisotropic diffusion and application to image processing
Full text linkAnisotropic diffusion is a well recognized tool in digital image processing, including edge detection and focusing. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for the space variable. In just a single step, the procedure emphasizes the contour lines encircling the objects, paving the way to accurate reconstructions at a very low cost. One of the main features of such an approach is the possibility of relying on a rather large set of invariant discontinuous images, whose edges can be determined without introducing any approximation
An Anisotropic Diffusion Algorithm for Image Deblurring
No full textThis paper deals with the problem of image deblurring. A suitable discretization scheme for a particular nonlinear time-dependent partial differential equation of parabolic type is experimented. The method is implemented by reversing the arrow of time in order to damp diffusion. Only one step is enough to reconstruct the edges of a corrupted picture affected by average blur. Thus, the procedure turns out to be extremely efficient
Electromagnetic fields simulating a rotating sphere and its exterior with implications to the modeling of the heliosphere
Full text linkVector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a ball. The fields satisfy the set of Maxwell's equations, and some connections with magnetohydrodynamics can also be established. The solutions are extended with continuity outside the ball. In order to avoid peripheral velocities of arbitrary magnitude, as it may happen for a rigid rotating body, they are organized to form successive encapsulated shells, with substructures recalling ball-bearing assemblies. A recipe for the construction of these solutions is provided by playing with the eigenfunctions of the vector Laplace operator. Some applications relative to astronomy are finally discussed
The use of grossone in elastic net regularization and sparse support vector machines
Full text linkNew algorithms for the numerical solution of optimization problems involving the l0 pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral ⃝1 (grossone) and indicating the number of elements of the set IN, of natural numbers. We show how the numerical system built upon ⃝1 and the proposed approximation of the l0 pseudo-norm in terms of ⃝1 can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems
On the use of Hermite functions for the Vlasov–Poisson system
No full textWe apply a second-order semi-Lagrangian spectral method for the Vlasov–Poisson system, by implementing Hermite functions in the approximation of the distribution function with respect to the velocity variable. Numerical tests are performed on a standard benchmark problem, namely the two-stream instability test case. The approach uses two independent sets of Hermite functions, based on Gaussian weights symmetrically placed with respect to the zero velocity level. An experimental analysis is conducted to detect a reasonable location of the two weights in order to improve the approximation properties
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