NUMERICAL PROCEDURE OF ADDRESSING THE OPTIMAL STOPPING TIME OF EMPlOYER’S PROFILE FORMATION OPTION

Georgios Dimakos (Greece) and Athina Karantzi (Greece)

Received June 6, 2008

Abstract

The objective of this paper is to provide an application of optimal stopping theory on the employee’s professional profile formation space in a finite time interval This is illustrated by presenting specific numerical examples. We address the optimal time of termination of education by maximizing the employer’s expected discounted profits. The problem of addressing the maximum of employer’s profit is solved by constructing the Snell Envelope of employer’s stochastic process of the formation discount payoff. Also, the simple binomial Cox-Ross- Rubinstein pricing model is being used to show how the employer’s (investor) profile formation option can be priced using an equivalent measure for which the discounted price process is a martingale. Finally, it is proved that the editor (employer-state) of the profile formation option has at his disposal a strategy of hedging. That is to say, there is an admissible self-financing strategy (and the martingale measure is unique), which when followed the editor is hedged.

Keywords and phrases: optimal stopping theory, Martingale, price theory and market structure.