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.

A note on convergence of Peck-Shell and Green-Lin mechanisms in the Diamond-Dybvig model

We study the effects of population size in the Peck-Shell analysis of bank runs. We find that a contract featuring equal-treatment for almost all depositors of the same type approximates the optimum. Because the approximation also satisfies Green-Lin incentive constraints, when the planner discloses positions in the queue, welfare in these alternative specifications are sandwiched. Disclosure, however, it is not needed since our approximating contract is not subject to runs.

Convergence in Brazil: recent trends and long run prospects

This paper applies to the analysis of the interstate income distribution in BraziI a set of techniques that have been widely used in the current empirical literature on growth and convergence. Usual measures of dispersion in the interstate income distribution (the coefficient of variation and Theil' s index) suggest that cr-convergence was an unequivoca1 feature of the regional growth experience in BraziI, between 1970 and 1986. After 1986, the process of convergence seems, however, to have sIowed down almost to a halt. A standard growth modeI is shown to fit the regional data well and to expIain a substantial amount of the variation in growth rates, providing estimates of the speed of (conditional) J3-convergence of approximateIy 3% p.a .. Different estimates of the long run distribution implied by the recent growth trends point towards further reductions in the interstate income inequality, but also suggest that the relative per capita incomes of a significant number of states and the number of ''very poor" and "poor" states were, in 1995, already quite c10se to their steady-state values.