Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Stochastic responses and marginal valuation.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Robust inattentive discrete choice.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Estimating the spatial amplification of damage caused by degradation in the Amazon.

Proceedings of the National Academy of Sciences of the United States of America·2023
Same author

Rational policymaking during a pandemic.

Proceedings of the National Academy of Sciences of the United States of America·2021
Same author

Robust identification of investor beliefs.

Proceedings of the National Academy of Sciences of the United States of America·2020
Same author

Aversion to ambiguity and model misspecification in dynamic stochastic environments.

Proceedings of the National Academy of Sciences of the United States of America·2018

Related Experiment Video

Updated: May 20, 2026

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

Recursive utility in a Markov environment with stochastic growth.

Lars Peter Hansen1, José A Scheinkman

  • 1Departments of Economics and Statistics, University of Chicago, Chicago, IL 60637, USA.

Proceedings of the National Academy of Sciences of the United States of America
|July 11, 2012
PubMed
Summary

This study connects recursive utility models to Markov process eigenvalue equations. This link proves the existence and uniqueness of solutions for investor risk preferences in macroeconomics.

More Related Videos

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Phage Phenomics: Physiological Approaches to Characterize Novel Viral Proteins
09:40

Phage Phenomics: Physiological Approaches to Characterize Novel Viral Proteins

Published on: June 11, 2015

Related Experiment Videos

Last Updated: May 20, 2026

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli
15:00

Daily Transfers, Archiving Populations, and Measuring Fitness in the Long-Term Evolution Experiment with Escherichia coli

Published on: August 18, 2023

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

Phage Phenomics: Physiological Approaches to Characterize Novel Viral Proteins
09:40

Phage Phenomics: Physiological Approaches to Characterize Novel Viral Proteins

Published on: June 11, 2015

Area of Science:

  • Asset pricing
  • Macroeconomics
  • Stochastic processes

Background:

  • Recursive utility models are crucial in macroeconomics and asset pricing.
  • These models define preferences via nonlinear forward-looking difference equations with terminal conditions.

Purpose of the Study:

  • To analyze infinite-horizon recursive utility difference equations in Markov environments.
  • To establish a connection between these equations and Perron-Frobenius eigenvalue equations.

Main Methods:

  • Studying nonlinear forward-looking difference equations.
  • Utilizing Perron-Frobenius eigenvalue equations from Markov process theory.
  • Analyzing large deviation theory for stochastic processes.

Main Results:

  • Established a connection between recursive utility solutions and Perron-Frobenius eigenvalues.
  • Proved existence and uniqueness results for these models.
  • Linked large deviation bounds for tail events to recursive utility preferences.

Conclusions:

  • The connection simplifies analysis of recursive utility models.
  • Provides new insights into investor behavior concerning intertemporal risk.
  • Offers a novel framework for understanding tail risk in stochastic environments.