A Note on Markov Decision Process for Stock Option Model: a New Proof

Markov decision processes, also known as stochastic dynamic programs or stochastic controlproblems, are models for sequential decision making when outcomes are uncertain. In this paper,first, the stock option model is briefly introduced. Then, an optimality equation is obtained usingMarkov decision process. The optimality equation is a recursive equation and it is concluded that thereis no simple rule for obtaining an explicit solution for the optimality equation. Anyway, this equationhas some properties that yield the structure of the optimal policy. These properties are proved usinginduction approach. Finally application of this new proof is illustrated using two examples.

Keywords:

Markov decision process , Induction , Stock option , Dynamic Programming