Threshold structure of optimal stopping strategies for American type option. II. (English) Zbl 1102.91048

Jönsson, H.; Kukush, A. G.; Silvestrov, D. S.

Teor. Jmovirn. Mat. Stat. 72, 42-53 (2005) and Theory Probab. Math. Stat. 72, 47-58 (2006).

The authors study structure of the optimal stopping domains of the American type options in discrete time. In the first part of the paper [see H. Jönsson, A. G. Kukush and D. S. Silvestrov [Teor. Jmovirn. Mat. Stat. 71, 82–92 (2004) and Theory Probab. Math. Stat. 71, 93–103 (2005; Zbl 1101.91040)] the sufficient local conditions on the payoff functions and on the price process under which the stopping domains have one-threshold structure are derived. To model the payoff of general put options the authors use non-increasing and convex functions. In this part of the paper they give examples of put type payoff functions and the corresponding concrete form of sufficient conditions proposed in the first part of the paper.

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

91B28	Finance etc. (MSC2000)
62L15	Optimal stopping in statistics
60J25	Continuous-time Markov processes on general state spaces
60G40	Stopping times; optimal stopping problems; gambling theory
62P05	Applications of statistics to actuarial sciences and financial mathematics

Keywords:

threshold structure; optimal stopping strategy; American type option

Citations:

Zbl 1101.91040