An optimal time-management policy for labor supply and consumption decisions

The paper studies decisions regarding labor supply, consumption and cash savings that maximize the total utility of consumption and non-labor time of an individual. A new dynamic model that studies the relationship between time and wealth, with the goal of determining the optimal fractions of time an individual should allocate to three different types of activities: labor, consumption, and recreation, is developed. We analyze the optimality conditions, construct optimal solutions, and discuss their properties with respect to the division of time for two types of individuals, who can be characterized as consumption-averse and consumption-seeking. A consumption-averse individual does not enjoy shopping time, but when shopping spends money intensively. A consumption-seeking person does enjoy shopping time and spends money slowly. The difference in decision making of the two types of individuals is illustrated by comparing the optimal division of time at a singular regime that takes place over a substantial part of the planning horizon.     

Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces

We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on ?-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a topologically typical ?-periodic surface with a boundary are recurrent.     

The value iteration algorithm is not strongly polynomial for discounted dynamic programming

This note provides a simple example demonstrating that, if exact computations are allowed, the number of iterations required for the value iteration algorithm to find an optimal policy for discounted dynamic programming problems may grow arbitrarily quickly with the size of the problem. In particular, the number of iterations can be exponential in the number of actions. Thus, unlike policy iterations, the value iteration algorithm is not strongly polynomial for discounted dynamic programming.