5,012 research outputs found
Mild solutions to the dynamic programming equation for stochastic optimal control problems
We show via the nonlinear semigroup theory in that the
-D dynamic programming equation associated with a stochastic optimal control
problem with multiplicative noise has a unique mild solution with . The -dimensional case is also investigated
Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model
We study a family of mean field games with a state variable evolving as a
multivariate jump diffusion process. The jump component is driven by a Poisson
process with a time-dependent intensity function. All coefficients, i.e. drift,
volatility and jump size, are controlled. Under fairly general conditions, we
establish existence of a solution in a relaxed version of the mean field game
and give conditions under which the optimal strategies are in fact Markovian,
hence extending to a jump-diffusion setting previous results established in
[30]. The proofs rely upon the notions of relaxed controls and martingale
problems. Finally, to complement the abstract existence results, we study a
simple illiquid inter-bank market model, where the banks can change their
reserves only at the jump times of some exogenous Poisson processes with a
common constant intensity, and provide some numerical results.Comment: 37 pages, 6 figure
ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps
We consider a symmetric n-player nonzero-sum stochastic differential game with jump–diffusion dynamics and mean-field type interaction among the players. Under the assumption of existence of a regular Markovian solution for the corresponding limiting mean-field game, we construct an approximate Nash equilibrium for the n-player game for n large enough, and provide the rate of convergence. This extends to a class of games with jumps classical results in mean-field game literature. This paper complements our previous work Benazzol et al. (2017) on the existence of solutions of mean-field games for jump–diffusions
Minimal flavor-changing models and muon after the measurement
There has been a steady interest in flavor anomalies and their global fits as
ideal probes of new physics. If the anomalies are real, one promising
explanation is a new gauge boson with flavor-changing coupling to bottom
and strange quarks and a flavor-conserving coupling to muons and, possibly,
electrons. We point out that direct production of such a , emerging from
the collision of and quarks, may offer a complementary window into
these phenomena because collider searches already provide competitive
constraints. On top of that, we analyse the same scenario in relation to
another long-standing discrepancy between theory and experiment that concerns
the anomalous magnetic moment of the muon. By scanning the allowed
coupling strengths in the low-mass region, we assess the compatibility of the
signals from LHCb with the searches in the high energy LHC data and the
measurements of the anomalous magnetic moment of the involved leptons. We also
argue that observations of the latter can break the degeneracy pattern in the
Wilson coefficients and presented by LHCb data. The model
we consider is compatible with the new measurement of , therefore it
can potentially account for the long-standing deviations observed in
-physics.Comment: 13 pages, 5 figures. Missing factors corrected in eqs. 2.7-2.9 with
slight updates in fig.
An example of a three-type interference pattern in the Tuscan Nappe, South-western sector of Apuan Alps (Northern Apennines, Italy)
The study area is located in the Northern Apennines, which is composed of oceanic and continental-
derived tectonic units, stacked toward NE during Apennine subduction (Oligocene to
present). The continental-derived units, representative of the Adria paleomargin involved into
the collisional phases of the Alpine orogeny, are, from the lower to the upper structural levels:
the Apuan Alps Unit, the Massa Unit and the Tuscan Nappe.
The Apuan Alps Unit consists of pre-Mesozoic metamorphic basement and metasedimentary
cover rocks, ranging from Triassic to Oligocene, deformed and metamorphosed under greenschists
facies conditions. The Massa Unit, is also characterized by pre-Mesozoic metamorphic
basement unconformably covered by Middle to Upper Triassic metasedimentary rocks. It recorded
higher metamorphic conditions respect to underlying Unit. The Tuscan Nappe, instead, is
detached from its basement and it is composed by Late Triassic to Early Miocene nonmetamorphic
sedimentary rocks. This Unit was deformed at shallow structural levels.
In the southeastern sector of the Apuan Alps, sedimentary rocks of the Tuscan nappe crop out.
Particularly, in the study area, this unit includes only LateTriassic - Early Cretaceous rocks (Carosi
et al., 2005). Field observations and structural data allowed us to elaborate a 1:5.000 scale
structural map. Structural analyses highlighted a comlplex deformation history, composed by
five deformation events (from D1 to D5), documented a different scale. The D1 event is testified
by S1 foliation classifiable as slaty cleavage. In thin section, S1 is emphasised by preferential
orientation of phyllosilicates and lenticular domains composed of quartz, calcite, detrital micas,
albite and oxides. Open to isoclinal similar folds (F2) with NW-SE trending axes are associated
to the D2 event. F2 folds are associated to a well developed S2 axial plane classifiable as crenulation
cleavage without significant re-crystallisation. The D3 event is not well developed in this
area and it is locally recorded in the fine-grained rocks where it produced isoclinal folds with
scattered axes and axial planes oriented N-S. The previous architecture is reworked by folds
with chévron geometry and sub-horizontal axial plane associated to the D4 event. Finally, D5
event is characterized by open folds with sub-vertical axial plane and three systems of normal to
transtensive faults. These brittle structures, could be interpreted as conjugate faults of the Monte
Croce-Pescaglia faults system.
In conclusion, field observations and structural analysis conducted both at the micro and at the
mesoscopic scale, indicate that Tuscan Nappe exposed in the study area was affected by a kmscale
three-type interference pattern (Ramsay, 1967). Furthermore, our studies suggest that the
faults played a role of great importance in the present architecture of this sector of the belt
Default Contagion in Financial Networks
The preset work aims at giving insights about howthe theory behind the study of complex networks can be profitablyused to analyse the increasing complexity characterizinga wide number of current financial frameworks. In particularwe exploit some well known approaches developed within thesetting of the graph theory, such as, e.g., the Erd˝os and Rénymodel, and the Barab´asi-Albert model, as well as producingan analysis based on the evolving network theory. Numericalsimulations are performed to study the spread of financial peakevents, as in the case of the default of a single bank belonging toa net of interconnected monetary institutions, showing how theknowledge about the underlying graph theory can be effectivelyused to withstand a financial default contagion
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