Environmental risk assessments can provide high confidence of minimal risk by testing theories, "risk hypotheses", that predict the likelihood of unacceptable harmful events. The creation of risk hypotheses and a plan to test them is called problem formulation. Effective problem formulation seeks to maximize the possibility of detecting effects that indicate potential risk; if such effects are ...

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing velocity subintervals resulting linear parabolic for vorticity. Probabilistic representations solutions these are given. At each step, expressed via vorticity using formula corresponding to Biot--Savar...

We introduce a category that represents varying risk as well as ambiguity. We give a generalized conditional expectation as a presheaf for this category, which not only works as a traditional conditional expectation given a σ-field but also is compatible with change of measure. Then, we reformulate dynamic monetary value measures as a presheaf for the category. We show how some axioms of dynami...

The classical Quadratic Programming formulation of the well known portfolio selection problem, is cumbersome, time consuming and relies on two important assumptions: (a) the expected return is multivariate normally distributed; (b) the investor is risk averter. This paper formulates two alternative models, (i) maximin, and (ii) minimization of absolute deviation. Data from a very simple problem...

Owing to rising intentional events, supply chain disruptions have been considered by setting up a game between two players, namely, a designer and an interdictor contesting on minimizing and maximizing total cost, respectively. The previous studies have found the equilibrium solution by taking transportation, penalty and restoration cost into account. To contribute further, we examine how incor...

This paper makes explicit the links between preferences over lotteries on length of life and intertemporal choice. I show that the approach used by traditional life cycle models to account for uncertain survival corresponds to a strong assumption of risk neutrality with respect to the length of life. Relaxing such an assumption leads us to develop a more general formulation of lifetime utility ...