Study of undiscounted non-linear optimal multiple stopping problems on unbounded intervals. (English) Zbl 1390.60157

Trabelsi, Faouzi

Int. J. Math. Oper. Res. 5, No. 2, 225-254 (2013).

Summary: In this paper we formulate and solve a class of undiscounted non-linear optimal multiple stopping problems, where the underlying price process follows a general linear regular diffusion on an unbounded and closed subinterval of the state space and where the payoff/reward function is bounded, continuous and superadditive. We use and adapt general theory of optimal stopping for diffusion and we illustrate the developed optimal exercise strategies by the example of valuation of perpetual American-style fixed strike discretely random monitoring Asian put options on any unbounded closed interval of the form \([\varepsilon,\infty)\), where \(\varepsilon>0\) is a given lower bound.

MSC:

60G40

Stopping times; optimal stopping problems; gambling theory

Keywords:

nonlinear multiple stopping; optimal multiple stopping; regular linear diffusion; perpetual American-style options; fixed strike random monitoring Asian put; excessive functions