We apply numerical dynamic programming to multi-asset dynamic portfolio optimization problems with proportional transaction costs. Examples include problems with one safe asset plus two to six risky stocks, and seven to 360 trading periods in a finite horizon problem. These examples show that it...

We implement a dynamic programming algorithm on a computational grid consisting of loosely coupled processors, possibly including clusters and individual workstations. The grid changes dynamically during the computation, as processors enter and leave the pool of workstations. The algorithm is...

This Technical Note provides detailed information on the Brazilian risk classification system using the RI approach and the Indian RI system for the initial risk screening of a large portfolio of existing dams. Annex A provides basic information about the RI approach used in Quebec, Canada, for...

This survey report represents a collaborative effort between Reserve Advisory and Management Partnership (RAMP) and central banks worldwide to advance the understanding and practice of reserve management. The cooperation of all central banks involved is greatly appreciated, and we anticipate...

The World Bank Treasury's Reserve Advisory and Management Partnership (RAMP) conducted its third survey on reserve management practices in 2021. One hundred and nineteen central banks, from different regions, income groups, and reserve levels, contributed to the survey, which included questions...

Implicit contingent liabilities, such as those generated by natural disasters, are often not quantified in the government balance sheet. However, when they materialize, they place pressure on government finances that may raise interest expenditures and financial risks. Understanding the impacts...

The World Bank's VA and VASP ML/TF Risk Assessment Tool (VA-RA) and this Guidance, aims to assist countries in assessing the ML/TF risks of VA activities and the service providers in the financial and non-financial sectors involved in these activities. It outlines the steps and explanations to...

This paper extends two optimization routines to deal with objective functions for DSGE models. The optimization routines are i) a version of Simulated Annealing developed by Corana, Marchesi & Ridella (1987), and ii) the evolutionary algorithm CMA-ES developed by Hansen, Müller & Koumoutsakos...

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data is easily obtained from solving the Bellman equation and can be used to approximate value functions. We illustrate this method with one-, three-, and...

An enhanced version of a structural model jointly explains benefit claiming, wealth and retirement, including reversals from states of lesser to greater work. The model includes stochastic returns on assets. Estimated with Health and Retirement Study data, it does a better job of predicting...