Optimal multiple stopping time problem

By M. Kobylanski, Marie Claire Quenez, Elisabeth Rouy-Mironescu. 2009

61 citations recorded by the source corpus.

We study the optimal multiple stopping time problem defined for each stopping time $S$ by $\displaystyle{ v(S)=\esssup_ {\tau_1,\cdots,\tau_d \geq S } E[\psi( \tau_1,\cdots,\tau_d)\, |\,\F_S]\,}$.\\ The key point is the construction of a {\em new reward} $\phi$ such that the value function $v(S)$ satisfies also $ v(S)=\esssup_ {\theta \geq S } \,E[\phi(\theta)\, |\,\F_S]\,.$ This new reward $\phi$ is not a right continuous adapted process as in the classical case but a family of random variables. For such a reward, we prove a new existence result of optimal stopping times under weaker assumptions than in the classical case. This result is used to prove the existence of optimal multiple stopping times for $v(S)$ by a constructive method. Moreover, under strong regularity assumptions on $\psi$, we show that the new reward $\phi$ can be aggregated by a progressive process. This leads to different applications in particular in finance for American options with multiple exercise times.

Subfields: Computer Networks and Communications, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a950e5443bd8900f790872352a012d27798408bf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Finance

In Management Science and Operations Research

Citations in the corpus

Optimal stopping with f-expectations: The irregular case (2016, methodology): “mily V = (V(S),S ∈ T0,T) deﬁned in (5.21) is a square-integrable admissible family. The proof uses arguments similar to those used in the "classical" case of linear expectations (cf., e.g., [24]), combined with some properties of f-expectations. Proof: For each S ∈ T0,T, V(S) is an FS-meas”