We characterize the extremal structures for certain random walks on trees. Let G = (V,E) be a tree with stationary distribution π. For a vertex i ∈ V , let H(π, i) and H(i, π) denote the expected lengths of optimal stopping rules from π to i and from i to π, respectively. We show that among all trees with |V | = n, the quantities mini∈V H(π, i), maxi∈V H(π, i), maxi∈V H(i, π) and ∑ i∈V πiH(i, π...

The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading in all assets is subject to proportional transaction costs, and where the existence of a risk-free numéraire is not assumed. Probabilistic dual representations are obtained for the bid and ask prices of such opt...

The critical step facing every decision maker is when to stop collecting evidence and proceed with the decision act. This is known as the stopping rule. Over the years, several unconnected explanations have been proposed that suggest nonoptimal approaches can account for some of the observable violations of the optimal stopping rule. The current research proposes a unifying explanation for thes...

This paper deals with Bruss’ odds problem with multiple stopping chances. A decision maker observes sequentially a sequence of independent 0/1 (failure/success) random variables with the objective to predict the last success correctly with multiple stopping chances. First, we give a nontrivial lower bound of the probability of win (obtaining the last success) for the problem with m-stoppings. N...

h a stochastic and fuzzy environment, a multiobjective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and linear ranking functions, respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using X-optimal stopping times. @ 2003 Elsevier Ltd. All rights reserved. &Fords-Mul...

In a stochastic and fuzzy environment, two kinds of stopping models are discussed and compared. The optimal fuzzy stopping times are given under the assumptions of monotonicity and regularity for stopping rules. Also, we find that fuzzy stopping times are favored in a comparison between fuzzy and classical stopping models. Q 2000 Academic Press