13. To Infinity … and Beyond

This chapter delves into the world of infinite-horizon problems in dynamic programming, highlighting their advantages and applications. It begins by exploring the concept of stationarity and how it simplifies the analysis of such problems. The text then introduces Bellman's equation and discusses two approaches to solving dynamic programming problems: value iteration and policy iteration. The chapter applies these concepts to the practical problem of harvesting trees from a forest, illustrating how infinite-horizon problems can be used to determine the optimal rotation length for maximizing the value of forest land. It also introduces the Faustmann model, a classic approach to forest management that considers an infinite series of timber rotations. The chapter concludes with a detailed example of policy iteration, demonstrating how to determine the best policy for a farmer battling invasive weeds. This example illustrates the power of dynamic programming in solving real-world problems with probabilistic and intertemporal elements.