194 research outputs found
Solving the relativistic inverse stellar problem through gravitational waves observation of binary neutron stars
The LIGO/Virgo collaboration has recently announced the direct detection of
gravitational waves emitted in the coalescence of a neutron star binary. This
discovery allows, for the first time, to set new constraints on the behavior of
matter at supranuclear density, complementary with those coming from
astrophysical observations in the electromagnetic band. In this paper we
demonstrate the feasibility of using gravitational signals to solve the
relativistic inverse stellar problem, i.e. to reconstruct the parameters of the
equation of state (EoS) from measurements of the stellar mass and tidal Love
number. We perform Bayesian inference of mock data, based on different models
of the star internal composition, modeled through piecewise polytropes. Our
analysis shows that the detection of a small number of sources by a network of
advanced interferometers would allow to put accurate bounds on the EoS
parameters, and to perform a model selection among the realistic equations of
state proposed in the literature.Comment: minor changes to match the version published on PR
From micro to macro and back: probing near-horizon quantum structures with gravitational waves
Supermassive binaries detectable by the future space gravitational-wave
interferometer LISA might allow to distinguish black holes from ultracompact
horizonless objects, even when the latter are motivated by quantum-gravity
considerations. We show that a measurement of very small tidal Love numbers at
the level of accuracy (as achievable with "golden binaries") may also
allow to distinguish between different models of these exotic compact objects,
even when taking into account an intrinsic uncertainty in the object radius
putatively due to quantum mechanics. We argue that there is no conceptual
obstacle in performing these measurements, the main challenge remains the
detectability of small tidal effects and an accurate waveform modelling. Our
analysis uses only coordinate-independent quantities related to the proper
radial distance and the total mass of the object.Comment: Minor changes to match the version published on CQ
Probing Planckian corrections at the horizon scale with LISA binaries
Several quantum-gravity models of compact objects predict microscopic or even
Planckian corrections at the horizon scale. We explore the possibility of
measuring two model-independent, smoking-gun effects of these corrections in
the gravitational waveform of a compact binary, namely the absence of tidal
heating and the presence of tidal deformability. For events detectable by the
future space-based interferometer LISA, we show that the effect of tidal
heating dominates and allows one to constrain putative corrections down to the
Planck scale. The measurement of the tidal Love numbers with LISA is more
challenging but, in optimistic scenarios, it allows to constrain the
compactness of a supermassive exotic compact object down to the Planck scale.
Our analysis suggests that highly-spinning, supermassive binaries at 1-20 Gpc
provide unparalleled tests of quantum-gravity effects at the horizon scale.Comment: v4: matches version in Phys. Rev. Lett; Editors' Suggestio
Optimal Dividend Payout under Stochastic Discounting
Bandini E, de Angelis T, Ferrari G, Gozzi F. Optimal Dividend Payout under Stochastic Discounting. Center for Mathematical Economics Working Papers. Vol 636. Bielefeld: Center for Mathematical Economics; 2020.Adopting a probabilistic approach we determine the optimal dividend
payout policy of a firm whose surplus process follows a controlled arithmetic Brownian
motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends
can be paid to shareholders at unrestricted rates so that the problem is cast as one of
singular stochastic control. The stochastic interest rate is modelled by a Cox-Ingersoll-
Ross (CIR) process and the firm's objective is to maximize the total expected flow of
discounted dividends until a possible insolvency time.
We find an optimal dividend payout policy which is such that the surplus process is
kept below an endogenously determined stochastic threshold expressed as a decreasing
function of the current interest rate value. We also prove that the value
function of the singular control problem solves a variational inequality associated to
a second-order, non-degenerate elliptic operator, with a gradient constraint.2010 Mathematics Subject Classification. 91G50, 93E20, 60G40, 35R3
A Nonconvex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries
Abstract. Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping; see, for example, Karatzas and Shreve [SIAM J. Control Optim., 22 (1984), pp. 856–877]. The aim of this paper is to inves-tigate how far connections of this type generalize to a nonconvex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a nonconvex infinite time horizon SSC problem whose state consists of an un-controlled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyze the geometry of the action and inaction regions by characterizing their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping
On the Singular Control of Exchange Rates
Ferrari G, Vargiolu T. On the Singular Control of Exchange Rates . Center for Mathematical Economics Working Papers. Vol 594. Bielefeld: Center for Mathematical Economics; 2017.Consider the problem of a central bank that wants to manage the exchange
rate between its domestic currency and a foreign one. The central bank can
purchase and sell the foreign currency, and each intervention on the exchange market
leads to a proportional cost whose instantaneous marginal value depends on the
current level of the exchange rate. The central bank aims at minimizing the total
expected costs of interventions on the exchange market, plus a total expected holding
cost. We formulate this problem as an infinite time-horizon stochastic control problem
with controls that have paths which are locally of bounded variation. The exchange
rate evolves as a general linearly controlled one-dimensional diffusion, and the two
nondecreasing processes giving the minimal decomposition of a bounded-variation
control model the cumulative amount of foreign currency that has been purchased
and sold by the central bank. We provide a complete solution to this problem by
finding the explicit expression of the value function and a complete characterization
of the optimal control. At each instant of time, the optimally controlled exchange rate
is kept within a band whose size is endogenously determined as part of the solution to
the problem. We also study the expected exit time from the band, and the sensitivity
of the width of the band with respect to the model's parameters in the case when
the exchange rate evolves (in absence of any intervention) as an Ornstein-Uhlenbeck
process, and the marginal costs of controls are constant. The techniques employed in
the paper are those of the theory of singular stochastic control and of one-dimensional diffusion
Stochastic nonzero-sum games: a new connection between singular control and optimal stopping
de Angelis T, Ferrari G. Stochastic nonzero-sum games: a new connection between singular control and optimal stopping . Center for Mathematical Economics Working Papers. Vol 565. Bielefeld: Center for Mathematical Economics; 2016.In this paper we establish a new connection between a class of 2-player nonzerosum
games of optimal stopping and certain 2-player nonzero-sum games of singular control. We
show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at
two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of
singular control. Moreover a differential link between the players' value functions holds across
the two games
Stochastic nonzero-sum games: a new connection between singular control and optimal stopping
de Angelis T, Ferrari G. Stochastic nonzero-sum games: a new connection between singular control and optimal stopping . Center for Mathematical Economics Working Papers. Vol 565. Bielefeld: Center for Mathematical Economics; 2016.In this paper we establish a new connection between a class of 2-player nonzerosum
games of optimal stopping and certain 2-player nonzero-sum games of singular control. We
show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at
two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of
singular control. Moreover a differential link between the players' value functions holds across
the two games
A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis
de Angelis T, Ferrari G. A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis. Center for Mathematical Economics Working Papers. Vol 477. Bielefeld: Center for Mathematical Economics; 2013.We study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional,time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investment-disinvestment
problem a zero-sum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries
- …