We present a satisfactory definition of the important class of Lévy processes indexed by a general collection of sets. We use a new definition for increment stationarity of set-indexed processes to obtain different characterizations of this class. As an example, the set-indexed compound Poisson...

Abstract We consider a sequential testing problem of three hypotheses that the unknown drift of a Brownian motion takes one of three values. We show that this problem can be solved by a reduction to an optimal stopping problem for local times of the observable process. For the case of...

A mathematical model of competitive selection of the applicants for a post is considered. There are N applicants of similar qualifications on an interview list. The applicants come in a random order and their salary demands are distinct. Two managers, I and II, will interview them one at a time....

We present the solution of a portfolio optimization problem for an economic agent endowed with a stochastic insurable stream, under a liquidity constraint over the time interval [0,T]. Generally, the existence of labor income complicates the agent's decisions. Moreover, in the real world the...

On the commodity market there exist contracts which give the holder multiple opportunities to adjust delivery of the underlying commodity. These contracts are often named “Swing” or “take-or-pay” options. They are especially common on the electricity market. In this paper the price of a...

Many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty. Motivated by experimental evidence such as the Ellsberg Paradox, we follow Knight (1921) and distinguish risk from uncertainty. To afford this distinction, we adopt the multiple-priors...

The valuation of a Swing option for stocks under the additional constraint of a minimum time distance between two different exercise times is considered. We give an explicit characterization of its pricing function as the value function of a multiple optimal stopping problem. The solution of...