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Risk exchange with distorted probabilities
An exchange economy is considered,where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities.Pricing formulas and risk allocations,generalising the results of BĂŒhlmann (1980,1984) are obtained via the construction of aggregate preferences from heterogeneous agentsâ utility and distortion functions. This involves the introduction of a novel âcollective ambiguity aversionâ coefficient. It is shown that probability distortion changes insurersâbehaviour, who trade not only to share the aggregate market risk, but are also found to bet against each other.Moreover,probability distortion tends to increase the price of insurance (increase asset returns). While the cases of rank-dependence and ambiguity are formally similar,an important distinction emerges as for rank-dependent preferences equilibria are determinate, while for ambiguity they are generally indeterminate
Some results on dependent random variables and a connection with the multivariate s-increasing convex order
In this paper some new concepts of dependence are introduced that generalize the concepts of positive and negative association. The new concepts of dependence are linked to the multivariate s-increasing convex order (Denuit and Mesfioui (2010, 2013)). Furthermore, a Kolmogorov-type inequality and a Hajek-Renyi inequality are proven that lead to an asymptotic
result for these new random objects
HESS Opinions: "Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability"
Since 1990 extensive funds have been spent on
research in climate change. Although Earth Sciences, including
climatology and hydrology, have benefited significantly,
progress has proved incommensurate with the effort
and funds, perhaps because these disciplines were perceived
as âtoolsâ subservient to the needs of the climate change enterprise
rather than autonomous sciences. At the same time,
research was misleadingly focused more on the âsymptomâ,
i.e. the emission of greenhouse gases, than on the âillnessâ,
i.e. the unsustainability of fossil fuel-based energy production.
Unless energy saving and use of renewable resources
become the norm, there is a real risk of severe socioeconomic
crisis in the not-too-distant future. A framework for drastic
paradigm change is needed, in which water plays a central
role, due to its unique link to all forms of renewable energy,
from production (hydro and wave power) to storage (for
time-varying wind and solar sources), to biofuel production
(irrigation). The extended role of water should be considered
in parallel to its other uses, domestic, agricultural and
industrial. Hydrology, the science of water on Earth, must
move towards this new paradigm by radically rethinking its
fundamentals, which are unjustifiably trapped in the 19thcentury
myths of deterministic theories and the zeal to eliminate
uncertainty. Guidance is offered by modern statistical
and quantum physics, which reveal the intrinsic character of
uncertainty/entropy in nature, thus advancing towards a new
understanding and modelling of physical processes, which is
central to the effective use of renewable energy and water
resources
Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots
A graph environment must be explored by a collection of mobile robots. Some
of the robots, a priori unknown, may turn out to be unreliable. The graph is
weighted and each node is assigned a deadline. The exploration is successful if
each node of the graph is visited before its deadline by a reliable robot. The
edge weight corresponds to the time needed by a robot to traverse the edge.
Given the number of robots which may crash, is it possible to design an
algorithm, which will always guarantee the exploration, independently of the
choice of the subset of unreliable robots by the adversary? We find the optimal
time, during which the graph may be explored. Our approach permits to find the
maximal number of robots, which may turn out to be unreliable, and the graph is
still guaranteed to be explored.
We concentrate on line graphs and rings, for which we give positive results.
We start with the case of the collections involving only reliable robots. We
give algorithms finding optimal times needed for exploration when the robots
are assigned to fixed initial positions as well as when such starting positions
may be determined by the algorithm. We extend our consideration to the case
when some number of robots may be unreliable. Our most surprising result is
that solving the line exploration problem with robots at given positions, which
may involve crash-faulty ones, is NP-hard. The same problem has polynomial
solutions for a ring and for the case when the initial robots' positions on the
line are arbitrary.
The exploration problem is shown to be NP-hard for star graphs, even when the
team consists of only two reliable robots
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