Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time

2019 ◽  
Vol 128 ◽  
pp. 384-399 ◽  
Author(s):  
Farzad Alavi Fard ◽  
Malick Sy ◽  
Dmitry Ivanov
Keyword(s):  
Dynamic Programming ◽  
Continuous Time ◽  
Programming Approach ◽  
Dynamic Programming Approach

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.

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