Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Balance of payments dominance: its implications for macroeconomic policy

This paper defines “balance of payments dominance” as a macroeconomic regime in which the short-term macroeconomic dynamics is essentially determined by external shocks, positive or negative. It argues that this is the predominant regime in emerging and developing countries. Trade shocks play an important role but the major procyclical shocks are associated with boom-bust cycles in external financing. Policy challenges are associated not only with the management of such shocks but also with the need to enhance the space for countercyclical macroeconomic policies, as boom-bust cycles tend to pressure macroeconomic policies to behave in a procyclical way. Under these conditions, the best bet is to design policies to reduce external vulnerabilities through a mix of administered exchange rate policies, very active foreign exchange reserve management, reduced reliance on external borrowing, and macroprudential regulations, including those directly affecting capital flows. Countercyclical fiscal policy can also play a role but face strong economic and political economy challenges.

Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).

Balance of payments dominance : its implocations for macroeconomic policy

This paper defines “balance of payments dominance” as a macroeconomic regime in which the short-term macroeconomic dynamics is essentially determined by external shocks, positive or negative. It argues that this is the predominant regime in emerging and developing countries. Trade shocks play an important role but the major procyclical shocks are associated with boom-bust cycles in external financing. Policy challenges are associated not only with the management of such shocks but also with the need to enhance the space for countercyclical macroeconomic policies, as boom-bust cycles tend to pressure macroeconomic policies to behave in a procyclical way. Under these conditions, the best bet is to design policies to reduce external vulnerabilities through a mix of administered exchange rate flexibility, very active foreign exchange reserve management, reduced reliance on external borrowing, and macroprudential regulations, including those directly affecting capital flows. Countercyclical fiscal policy can also play a role but face strong economic and political economy challenges.

Macroeconomic constraints to growth of Brazilian economy diagnosis and some policy proposals

The recent process of accelerated expansion of the Brazilian economy was driven by exports and fixed capital formation. Although the pace of growth was more robust than in the 1990´s, we can still witness the existence of certain macroeconomic constraints to its continuation in the long run such as, for instance, the exchange rate overvaluation in particular since 2005, and in general the modus operandi of monetary policy. Such constraints may jeopardize the sustainability of the current pace of growth. Therefore, we argue that Brazil still lies in a trap made up of high interest and low exchange rates. The elimination of the exchange rate misalignment would bring about a great increase in the rate of interest, which on its turn would impact negatively upon investment and hence upon the sustainability of long run economic growth. We outline a set of policy measures to eliminate such a trap, in particular, the adoption of an implicit target for the exchange rate, capital controls and the abandonment of the present regime of inflation targeting. Recent events seem to go in this direction.