Optimal Stopping Theory and American Options

2019 ◽  
pp. 376-396
Author(s):  
Tomas Björk
Keyword(s):  
Dynamic Programming ◽  
Optimal Stopping ◽  
Continuous Time ◽  
American Options ◽  
Programming Approach ◽  
Free Boundary Value Problem ◽  
Snell Envelope ◽  
Dynamic Programming Approach ◽  
Optimal Stopping Theory ◽  
Time Theory

In this chapter we present the dynamic programming approach to optimal stopping problems. We start by presenting the discrete time theory, deriving the relevant Bellman equation. We present the Snell envelope and prove the Snell Envelope Theorem. For Markovian models we explore the connection to alpha-excessive functions. The continuous time theory is presented by deriving the free boundary value problem connected to the stopping problem, and we also derive the associated system of variational inequalities. American options are discussed in some detail.

EQUILIBRIUM IN n-PERSON GAME OF SHOWCASE SHOWDOWN

2010 ◽  
Vol 24 (3) ◽  
pp. 397-403 ◽  
Author(s):  
Vladimir Mazalov ◽  
Anna Ivashko
Keyword(s):  
Dynamic Programming ◽  
Optimal Stopping ◽  
Random Variables ◽  
Programming Approach ◽  
Dynamic Programming Approach ◽  
Stopping Game ◽  
Level 1 ◽  
Person Game ◽  
Independent And Identically Distributed

In this article we consider a noncooperative n-person optimal stopping game of Showcase Showdown, in which each player observes the sum of independent and identically distributed random variables uniformly distributed in [0, 1]. Players can decide to stop the draw in each moment. The objective of a player is to get the maximal number of scores that does is not exceeded level 1. If the scores of all players exceed 1, then the winner is the player whose score is closest to 1. We derive the equilibrium in this game on the basis of the dynamic programming approach.

Sign in / Sign up

Export Citation Format

Share Document