This book mixes tools and sample applications. Our philosophy is to present the tools with enough technical sophistication for our applications, but little more. We aim to give readers a taste of the power of the methods and to direct them to sources where they can learn more.

Recursive methods constitute a powerful approach to dynamic economics due to their described focus on a tradeoff between the current period’s utility and a continuation value for utility in all future periods. As mentioned, the simplification arises from dealing with the evolution of state variables that capture the consequences of today’s actions and events for all future periods, and in the case of uncertainty, for all possible realizations in those future periods. This is not only a powerful approach to characterizing and solving complicated problems, but it also helps us to develop intuition, conceptualize, and think about dynamic economics. Students often find that half of the job in understanding how a complex economic model works is done once they understand what the set of state variables is. Thereafter, the students are soon on their way to formulating optimization problems and transition equations. Only experience from solving practical problems fully conveys the power of the recursive approach. This book provides many applications.

这本书混合了工具和示例应用程序。我们的理念是为我们的应用程序提供足够的技术成熟度，但仅此而已。我们的目的是让读者领略到这些方法的力量，并引导他们找到可以学到更多的资料。

递归方法是动态经济学的一个强有力的方法，因为它们所描述的重点是在当前时期的效用和未来所有时期效用的连续值之间进行权衡。如前所述，简化来自于处理状态变量的演变，这些变量捕捉了今天的行动和事件对所有未来时期的影响，以及在不确定的情况下，对于这些未来时期内所有可能实现的结果。这不仅是描述和解决复杂问题的有力方法，而且有助于我们发展直觉、概念化和思考动态经济学。学生们经常发现，一旦他们了解了状态变量的集合，了解复杂经济模型如何运作的一半工作就完成了。从那以后，学生们很快就开始着手制定最优化问题和过渡方程。只有解决实际问题的经验才能充分传达递归方法的威力。这本书提供了许多应用程序。