How much do you know about the Bellman equation and dynamic programming?

Study Notes

Bellman equation is a necessary condition for optimality associated with dynamic programming
It is named after Richard E. Bellman
The equation applies to algebraic structures with a total ordering
In continuous-time optimization problems, the analogous equation is a partial differential equation called the Hamilton–Jacobi–Bellman equation
Dynamic programming breaks a multi-period planning problem into simpler steps at different points in time
The optimal plan is described by finding a rule that tells what the controls should be, given any possible value of the state
The optimal decision rule is the one that achieves the best possible value of the objective
Bellman showed that a dynamic optimization problem in discrete time can be stated in a recursive, step-by-step form known as backward induction by writing down the relationship between the value function in one period and the value function in the next period
The appropriate Bellman equation can be found by introducing new state variables (state augmentation)
The resulting augmented-state multi-stage optimization problem has a higher dimensional state space than the original multi-stage optimization problem - an issue that can potentially render the augmented problem intractable due to the “curse of dimensionality”
The Bellman equation is used in dynamic programming to solve optimization problems.
It simplifies the problem significantly when the variable is governed by a Markov process.
The resulting optimal policy function is measurable.
The Bellman equation takes a similar form for a general stochastic sequential optimization problem.
Martin Beckmann and Richard Muth were the first to apply the Bellman equation in economics.
Robert C. Merton's intertemporal capital asset pricing model is a celebrated economic application of the Bellman equation.
Dynamic programming is referred to as a "recursive method" in economics.
Recursive economics is a subfield of economics that uses dynamic programming.
Nancy Stokey, Robert E. Lucas, and Edward Prescott describe stochastic and nonstochastic dynamic programming in considerable detail.
Dynamic programming is employed to solve a wide range of theoretical problems in economics.
Dixit and Pindyck showed the value of dynamic programming for capital budgeting.
Anderson adapted the technique for business valuation.
Informational difficulties arise when choosing the discount rate.
Computational issues include the curse of dimensionality.
A Bellman equation is a recursion for expected rewards in Markov decision processes.
The equation describes the expected reward for following a fixed policy.
The Bellman optimality equation is for the optimal policy.
The equation describes the reward for taking the action with the highest expected return.
Miranda and Fackler, and Meyn 2007 discuss computational issues.
The technique can be applied to privately held businesses.

Description

Think you know all about the Bellman equation and dynamic programming? Test your knowledge with this quiz! From understanding the basics of the equation to its applications in economics and business valuation, this quiz covers it all. See how much you know about the necessary conditions for optimality associated with dynamic programming, the relationship between the value function in one period and the next, and the challenges of computational issues and the curse of dimensionality. Don't miss out on the chance to test your knowledge and learn more about