Threshold structure of optimal stopping strategies for American type option. I. (English) Zbl 1101.91040

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

Teor. Jmovirn. Mat. Stat. 71, 82-92 (2004) and Theory Probab. Math. Stat. 71, 93-103 (2005).

The authors deal with studies of optimal stopping domains of American type options in discrete time. A general inhomogeneous discrete time stochastic Markov process is considered to model the underlying asset’s price \(S_{n}=A_{n}(S_{n-1},Y_{n})\), \(n=1,\ldots,N\), where \(A_{n}(x,y)\), \(n=1,\ldots,N\) is a measurable function acting on \(R^{+}\times Y\) to \(R^{+}\), \(R^{+}=[0,\infty)\), and \(Y\) is a measurable space. Here \(S_{n}\) is the stock price at moment \(n\) and \(Y_{n}\) is a sequence of independent random variables that take values in the space \(Y\). The sufficient conditions on the price process and on the payoff functions under which the stopping domains have a one-threshold structure \(\Gamma_{n}=[0,d_{n}]\) with \(d_{n}<\infty\), \(n=0,\ldots,N-1,\) are derived. To model the payoff of a general put option the authors use non-increasing and convex functions.

Reviewer: A. D. Borisenko (Kyïv)

MSC:

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

Keywords:

threshold structure; optimal stopping strategies; American type option

Software:

OptAn