Minimum impatience theorems for recursive economic models
This book contributes to the lively discussion about the reasons for and thepossible implications of the occurrence of non-linear phenomena and chaos indynamic economic systems. The author takes a fresh look at intertemporal decision problems and shows how the time preference rate of the decision maker relates to the dynamic complexity of the optimal paths. It turns out that in order to get complicated or chaotic optimal paths the decision maker has to be sufficiently impatient. In this sense, the Minimum Impatience Theorems supplement the existing literature on "turnpike theorems" and global asymptotic stability of normative economic systems. The framework in which the results are derived is a very general dynamic optimization problem with recursive (stationary) utility functionals. Both the case where time is a discrete variable and the case of continuous time models are treated.
In this article we study monotone stochastic orders for real-valued processes with independent increments and derive sufficient deterministic conditions which are easy to verify and suitable for applications. Our proof is based on an explicit construction of a coupling. We also derive comparison results for L\'evy processes and semimartingales with conditionally independent increments.