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...

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the inital irregular optimal stopping problem to an...

In this paper the stop-waiting strategy of Franz Bruss is set into a simple probabilistic framework and applied to the apple share prices from 1984 to 2013. Within the probabilistic framework a heuristic and a mathematical decision rule using the $\Psi$ function is developed. The results are in...

Where is the most likely position for the last success in n events, if each event has the same probability Pr(A)? What is the probability for the last success? This situation assumes returning successes which is different to the stop waiting problem where a single best event is assumed. We set...

Stress is ubiquitous in society. In our model, stressors translate into subjective stress via an appraisal process. Stress reduces instantaneous utility of an individual directly and via a cognitive load argument. Coping can be functional and under the control of the individual or more automatic...

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...

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...