Continuous-time stochastic games with a finite number of states have substantial computational and conceptual advantages over the more common discrete-time model. In particular, continuous time avoids a curse of dimensionality and speeds up computations by orders of magnitude in games with more...

There are two important rules to patent races: minimal accomplishment necessary to receive the patent and the allocation of the innovation benefits. We study the optimal combination of these rules. A planner, who cannot distinguish between competing firms in a multistage innovation race,...

This paper shows that perturbation methods can be applied to a DSGE model with incomplete markets and a finite but arbitrarily large number of heterogeneous agents. We develop a simple but general solution technique that handles many state and choice variables for each agent and thus has an...

We characterize and demonstrate a solution method for an optimal commodity (sales) tax problem consisting of multiple goods, heterogeneous agents, and a nonconvex policy maker optimization problem. Our approach allows for more dimensions of heterogeneity than has been previously possible,...

A nonlinear programming formulation is introduced to solve infinite horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to avoid inefficient discretization. Our numerical results show that this nonlinear...

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...

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...

There is great uncertainty about the impact of anthropogenic carbon on future economic wellbeing. We use DSICE, a DSGE extension of the DICE2007 model of William Nordhaus, which incorporates beliefs about the uncertain economic impact of possible climate tipping events and uses empirically...

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...

Continuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a...