## Optimal stopping and perpetual options for Lévy processes (2000)

Citations: | 22 - 2 self |

### BibTeX

@MISC{Mordecki00optimalstopping,

author = {Ernesto Mordecki and Ernesto Mordecki},

title = {Optimal stopping and perpetual options for Lévy processes},

year = {2000}

}

### OpenURL

### Abstract

Solution to the optimal stopping problem for a L'evy process and reward functions (e x \Gamma K) + and (K \Gamma e x ) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and infimum of the process killed at this rate. Closed forms of this solutions are obtained under the condition of positive jumps mixed-exponentially distributed. Results are interpreted as admissible pricing of perpetual American call and put options on a stock driven by a L'evy process, and a Black-Scholes type formula is obtained. Keywords and Phrases: Optimal stopping, L'evy process, mixtures of exponential distributions, American options, Derivative pricing. JEL Classification Number: G12 Mathematics Subject Classification (1991): 60G40, 60J30, 90A09. 1 Introduction and general results 1.1 L'evy processes Let X = fX t g t0 be a real valued stochastic process defined on a stochastic basis(\Omega ; F ; F = (F t ) t0 ; P ) that satisfy the usual conditions. A...