Topics in Stochastic Analysis and Optimization of Systems

Abstract

Specific aims of our projects have been to study the following topics: (1) Backward Stochastic Differential Equations with reflection and connection with Dynkin games; (2) A deterministic approach to discrete-time Dynkin games; (3) Singular control problems with application to irreversible investment; (4) Synchronization and optimality for d-armed bandit problems; (5) Adaptive control of a diffusion to a goal, and connection to a parabolic Monge-Ampere-type equation; (6) Backward Stochastic Differential Equations with Constraints on the gains-process; (7) Control and stopping of a diffusion process on an interval. Findings include establishing existence and uniqueness results for solutions to these problems and their analytical characterizations. These results are significant because they provide explicit ways of constructing solutions or even explicit expressions for optimal processes in the above problems.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1998
Accession Number
ADA358040

Entities

People

  • Ioannis Karatzas
  • Jaksa Cvitanic

Organizations

  • Columbia University

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Brownian Motion
  • Differential Equations
  • Diffusion
  • Equations
  • Game Theory
  • Intervals
  • Investments
  • Mathematical Analysis
  • Mathematics
  • Optimization
  • Probability
  • Random Variables
  • Real Variables
  • Reflection
  • Scientists
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Operations Research