Optimal stopping with dynamic variational preferences
In the classical optimal stopping problems (see [\textit{Y. S.~Chow, H.~Robbins} and \textit{D.~Siegmund}, Great expectations: the theory of optimal stopping. Boston etc.: Houghton Mifflin Company (1971; Zbl 0233.60044); \textit{G.~Peskir} and \textit{A.~Shiryaev}, Optimal stopping and free-boundary problems. Basel: Birkhäuser (2006; Zbl 1115.60001)]), the decision maker is searching for the stopping time \(\tau\) in some class which minimizes (or maximizes) the expected gain \(\operatorname{E}g(X_\tau)\), where \(g\) is a given utility function and \(\{X_t\}_{t\geq 0}\) is a well-defined stochastic process. This paper is devoted to the generalization of the optimal stopping problem when the underlined process is not fixed. Based on \textit{F. Riedel}'s [Econometrica 77, No. 3, 857--908 (2009; Zbl 1181.60064)] results the concept of variational supermartingales and variational Snell envelopes with an accompanying theory is introduced. The theory is illustrated by examples.
scientific article; zbMATH DE number 5965269
scientific article