01 / Reading Guide
Reading Guide
Who this book is for
For graduate economics students and advanced quantitative readers studying recursive decision problems. It offers a systematic mathematical route through problems that appear in finance, resource allocation and other economic applications. The stage and advanced difficulty reflect the proofs and modelling demands, even though selected numerical examples can be explored earlier.
Prerequisites
Linear algebra, probability, multivariable calculus and proof-based mathematics are recommended. Familiarity with Markov chains and basic programming helps with the examples and runnable code. Readers should connect an abstract operator with a concrete optimisation problem.
What it covers
Ten chapters progress through operators and fixed points, Markov dynamics, optimal stopping, Markov decision processes, stochastic discounting, valuation, recursive decision processes, abstract dynamic programming and continuous time. The finite-state setting makes important structures visible before the additional complications of general state spaces. Numerical results are useful when interpreted through the assumptions behind the relevant optimality argument.
How to use it
Write a small decision problem with explicit states, actions, rewards and transition probabilities. Derive its Bellman operator before running code. Check the assumptions used to establish convergence and compare two starting value functions. Explain why a numerical stopping rule is appropriate and how changing a probability affects the policy. Use the abstract chapters to recognise a shared structure across applications rather than memorising separate solution recipes.
Edition and sources
The authors’ free editions explicitly request citation of Cambridge’s 2025 Finite States book. Online/PDF revisions can differ from print. Finite-state theory is the scope here; general state spaces require the separate companion. Free access does not imply a Creative Commons license for the book.
