# Read e-book Optimality in Infinite Horizon Economies

1. Zaslavski : On a Class of Infinite Horizon Optimal Control Problems.
2. Infinite-horizon optimal control problems in economics.
3. Multicast Sockets: Practical Guide for Programmers (The Practical Guides)?

Access provided by: anon Sign Out. A terminal cost for economic model predictive control with local optimality Abstract: In this work, we design a terminal cost for economic model predictive control EMPC which preserves local optimality.

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• We first show, based on the strong duality and second order sufficient condition SOSC of the steady-state optimization problem, that the optimal operation of the system is locally equivalent to an infinite-horizon LQR controller. This lecture provides an introduction to LQ control and its economic applications.

These themes appear repeatedly below. Mathematically, LQ control problems are closely related to the Kalman filter Recursive formulations of linear-quadratic control problems and Kalman filtering problems both involve matrix Riccati equations.

## LQ Control: Foundations – Quantitative Economics

Classical formulations of linear control and linear filtering problems make use of similar matrix decompositions see for example this lecture and this lecture. In reading what follows, it will be useful to have some familiarity with matrix manipulations vectors of random variables dynamic programming and the Bellman equation see for example this lecture and this lecture For additional reading on LQ control, see, for example, [LS18] , chapter 5 [HS08a] , chapter 4 [HLL96] , section 3.

This can easily be overcome by adding a sufficiently large mean. Fortunately, we can easily circumvent this problem by adding an extra state variable.

### Deterministic and Stochastic Systems

Actually, the preceding discussion applies to all standard dynamic programming problems. Now consider the problem of the decision-maker in the second to last period. Data contradicted the constancy of the marginal propensity to consume. See, for example, [Fri56] or [MB54] One property of those models is that households purchase and sell financial assets to make consumption streams smoother than income streams. The household savings problem outlined above captures these ideas. Again, this relationship breaks down towards the end of life due to the zero final asset requirement These results are relatively robust to changes in parameters.

## Decentralization In Infinite Horizon Economies

However, the loss of generality is not as large as you might first imagine. One illustration is given below. An example infinite horizon problem is treated below. Once again, smooth consumption is a dominant feature of the sample paths. The asset path exhibits dynamics consistent with standard life cycle theory. Exercise 1 gives the full set of parameters used here and asks you to replicate the figure. It is arguably the case that this income process still contains unrealistic features.

## Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems

However, we can still use our LQ methods here by suitably linking two-component LQ problems. This is possible because, in the two separate periods of life, the respective income processes [polynomial trend and constant] each fit the LQ framework The basic idea is that although the whole problem is not a single time-invariant LQ problem, it is still a dynamic programming problem, and hence we can use appropriate Bellman equations at every stage. This process gives the entire life-time sequence of value functions and optimal policies.

The next figure shows one simulation based on this procedure. Once again, the dominant feature observable in the simulation is consumption smoothing. Assets peak at retirement and subsequently decline. This intuition turns out to be correct.

The following figures show simulations produced by solving the corresponding LQ problem. The key to this conversion is to choose the right state — which can be a bit of an art. We also manipulated the profit function slightly. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services. Economic literature: papers , articles , software , chapters , books. Pareto optimality and competitive equilibrium in infinite horizon economies.

Transforming an infinite horizon problem into a Dynamic Programming one

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