Abstract
The Merton problem is casting the classical consumer theory in a continuous time framework. Given an initial wealth and a set of capital assets whose prices follow correlated Ito processes, the consumer selects a lifetime consumption program that he most prefers. He selects the program that is optimal for him out of all feasible consumption programs that he can achieve by investing his available wealth continuously in a dynamically managed portfolio of the available capital assets. When the consumer's preference over consumption programs is represented by an additive (or even recursive) utility functional, then his optimization problem can be solved by dynamic programming. This problem and its solution are described in this entry.
| Original language | English |
|---|---|
| Title of host publication | Encyclopedia of Quantitative Finance |
| Publisher | wiley |
| Pages | 1-5 |
| Number of pages | 5 |
| ISBN (Electronic) | 9780470061602 |
| ISBN (Print) | 9780470057568 |
| DOIs | |
| State | Published - 1 Jan 2010 |
Bibliographical note
Publisher Copyright:© 2010 John Wiley & Sons, Ltd. All rights reserved.
Keywords
- Hamilton–Jacob–Bellman equation
- asset prices
- capital assets
- consumption
- continuous-time
- controls
- dynamic programming
- indirect utility of wealth
- intertemporal capital asset pricing
- investment
- ito processes
- lifetime utility
- optimal portfolio
- partial differential equation
- riskless asset
- securities
- self-financing
- shares
- stochastic differential equation
- wealth dynamics
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