A level-set approach for stochastic optimal control problems under controlled-loss constraints

We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for additional strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then apply a level-set approach. With this approach, the state constraints can be managed through an exact penalization technique

High-order filtered schemes for time-dependent second order HJB equations

In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the Monge-Amp\`ere partial differential equation, SIAM J. Numer. Anal., 51(1):423--444, 2013, and more recently applied by other authors to stationary or time-dependent first order Hamilton-Jacobi equations. For high order approximation schemes (where "high" stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. The work introduces a suitable local modification of these schemes by "filtering" them with a monotone scheme, such that they can be proven convergent and still show an overall high order behaviour for smooth enough solutions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests from mathematical finance, focussing also on the use of backward difference formulae (BDF) for constructing the high order schemes.Comment: 27 pages, 16 figures, 4 table

Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

We study the approximation of parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the problem to obtain well-posedness and regularity of a related switching system and the convergence of its components to the HJB equation. In particular, we show existence of a viscosity solution to the switching system by a novel construction of sub- and supersolutions and application of Perron's method. Error bounds for monotone schemes for the HJB equation are then derived from estimates near the boundary, where the standard regularisation procedure for viscosity solutions is not applicable, and are found to be of the same order as known results for the whole space. We deduce error bounds for some common finite difference and truncated semi-Lagrangian schemes

Affective mobilization and the culture of fear in Battlestar Galactica reimagined

Conferencias y Comunicaciones del primer Congreso Internacional de literatura fantástica y ciencia ficción, celebrado del 6 al 9 de mayo de 2008 en la Universidad Carlos III de Madri

A Gibbs sampling approach to maximum a posteriori time delay and amplitude estimations

Research concerned with underwater propagation in a shallow ocean environment is a growing area of study. In particular, the development of fast and accurate computational methods to estimate environmental parameters and source location is desired. In this work, only select features of the acoustic field are investigated, namely, the time delays and amplitudes of individual paths, the signal-to-noise ratio, and the number of multi-path arrivals. The amplitudes and delays contain pertinent information about the geometry associated with the environment of interest. Estimating the time delays and amplitudes of select paths in a manner that is both accurate and time efficient, however, is not a trivial task. A Gibbs Sampling Monte Carlo technique is proposed to recover these arrivals and their features. The method is tested on synthetic data as well as data from the Haro Straight experiment for the estimation of the number of arrivals, the amplitude and time delay associated with each arrival, and the variance of noise. Signals involved in shallow water propagation closely resemble signals obtained in other areas such as radar and communication problems. Therefore, the estimation techniques presented here may be useful in these, among several other, applications

An “approximate knowledge”: event transmission in the post-9/11 informational culture

The aim of the essay is to look back at 9/11 from the temporal perspective of 2011 and interpret it as a singularity, that is a moment of destabilization that hit the media sphere, accelerating an already existing shift in communication politics towards affective involvement. The dimension of pathic engagement that the televised images of 9/11 inspired, their becoming a source of collective emotional instability (i.e. a global “culture of fear”), has amplified preexisting modes of communication that relied on the energetic and mobilizing lure of audiovisual transmission. Rather than approaching 9/11 as a metaphysical occurrence, an absolute ‘event’ unencumbered by the territorializing pull of its own geopolitical genealogy, the essay engages with it as a phase boundary whose transformative impact can be sensed in the tactics of mobilization that inform contemporary communication practices

Who really benefits from export processing zones? Evidence from Nicaraguan municipalities

Export processing zones are popular trade policies in developing countries, but there is limited empirical evidence on their local effects. This paper examines the impact of their establishment on the levels of per capita expenditure across Nicaraguan municipalities for the period 1993 to 2009. Using the time and cross-section variation of park openings in a difference-in-differences framework, I find that on average consumption levels increased by 10 to 12 percent in treated municipalities. Yet, average effects mask significant disparities across the expenditure distribution. The results suggest that the policy benefited the upper-tail the most: expenditure levels increased by up to 25 percent at the 90th percentile. At the opposite of the distribution, only the bottom decile registered a small positive effect of close to 10 percent across the period

Performance of Ground Anchors Built in a Flysch Deposit

AbstractThe ultimate pull-out tensile load of ground anchors is strongly dependent onsoil nature,grout injection and effective stress state around the bulb. In this paper, the comparison between the results of conventional pull-out testson instrumented anchors built in a flysch formation and those of small scale pull-out tests performed in the laboratory,on undisturbed soil samples recovered at the depth of the anchor bulb,allowed to closely examine the skin friction that can be mobilizedin undrained conditionsat the soil-structure interface. The experiments highlight a strong scale effect, probably depending on the real size androughness ofthe lateral surface of the bulb. In fact, theirregular bulb profiledue to flysch features strongly contributes to the pull-outstrength

Debt overhang and sovereign debt restructuring

After the huge debt increases in the 1940s, due to the WWII, and in the 1980s due to the emerging markets’ debt crises, the debt overhang problem is once again at the center of the academic and political debate because of the recent debt crisis that affected the European countries in 2009. The debt overhang theory explains how an high level of debt distorts the optimal investment decisions and reduces government’s incentives, in the debtor country, to undertake the necessary "adjustment policies". A huge literature focuses on the negative effects deriving from a debt overhang condition. In particular, this kind of literature has been mostly used to describe and to study poor and less developed countries. Nowadays instead, the situation is quite different with the Greek case that represents a very peculiar and never experienced situation. Chapter 1 of the thesis starts with an introduction of the sovereign debt overhang problem. Then, since the aim is to study the possible policy interventions able to solve it, the focus is posed on sovereign debt restructuring as a resolution mechanism. A relief intervention can be considered, indeed, as a way to reduce the debt burden for a country struggling with an high level of debt. Descriptions of the restructuring process, of the macroeconomic consequences and of the Greek case are then provided in this chapter in addition to some stylised facts and an event analysis useful to communicate the main messages. In the past, several different strategies of debt restructuring have been implemented and the consequences they produced were often different case by case. It is then interesting to study the effectiveness of the several options that can be used to restructure public debt. For this reason, a very simple theoretical model is developed in Chapter 2 in order to study three different strategies that can be used to solve a sovereign debt overhang problem. In particular, two strategies are based on a debt restructuring process, via face value reduction or rescheduling, whereas a third one is based on conditional-additional official lending. This strategy relies on the idea that the debtor country can benefit of new lending from the official sector, in order to undertake a larger amount of investment. The aim of the model is to represent schematically the functioning of the three restructuring processes to gain insights into their differences and to study their consequences in term of incentives to invest in a "troubled country". An empirical evidence of the debt overhang hypothesis is then provided in Chapter 3. The combination of the sovereign debt crisis of 2009 and the fiscal consolidation policies implemented as a result, makes indeed interesting to study this hypothesis in Europe. The Chapter exploits then a panel dataset for the European countries, between 1995 and 2015, in order to examine the extent to which increased levels of public debt have led to reduced public investment. We start the analysis from basic POLS models and then we expand it gradually to FE, IV and GMM estimation models. The results validate the debt overhang hypothesis and remain robust across various model specifications

Optimal management of pumped hydroelectric production with state constrained optimal control

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, "State-constrained stochastic optimal control problems via reachability approach", SIAM J. Control and Optim. 54 (5) (2016) , we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments