A Random Walk Subject to a Randomly Changing Environment.

Abstract

A common model for the changes over time of the price (or sometimes the logarithm of the price) of a commodity is the random walk model. This is a Markov model which supposes that the change in price in any time period is a random variable, independent of the past, and having a given distribution F. In this note, we propose a generalized model in which the distribution of price change at any time depends upon the (environmental state' at that time. That is, we suppose that if sub Sn and sub Yn represent the price and the environmental state at time in n then, given sub Yn = i, sub Sn+1 - Sn is a random variable with distribution Fi. We also suppose that the environmental state changes in a Markovian fashion. An application of this model to a stock option example is presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1983
Accession Number
ADA133847

Entities

People

  • Sheldon M. Ross

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Air Force
  • California
  • Classification
  • Climate Change
  • Commodities
  • Environment
  • Industrial Engineering
  • Markov Models
  • Models
  • Operations Research
  • Probabilistic Models
  • Probability
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Security
  • United States

Fields of Study

  • Mathematics

Readers

  • Government Contracting/Procurement.
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms