8,533 research outputs found
Risk Management – Managing Risks, not Calculating Them
The expected utility approach to decision making advocates a probability vision of the world and labels any deviation from it ‘irrational’. This paper reconsiders the rationality argument and argues that calculating risks is not a viable strategy in an uncertain world. Alternative strategies not only can save considerable cognitive and computational resources, but are more ‘rational’ with view to the restricted definition of rationality applied by expected utility theorists. The alternative decision making model of risk management is presented and explained.
A FIC-based stabilized finite element formulation for turbulent flows
We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite
Increment Calculus (FIC) framework. In comparison to existing FIC approaches for fluids, this formulation
involves a new term in the momentum equation, which introduces non-isotropic dissipation in the direction of
velocity gradients. We also follow a new approach to the derivation of the stabilized mass equation, inspired by
recent developments for quasi-incompressible flows. The presented FIC-FEM formulation is used to simulate
turbulent flows, using the dissipation introduced by the method to account for turbulent dissipation in the style
of implicit large eddy simulation.Peer ReviewedPostprint (author's final draft
The Behavior of Savings and Asset Prices When Preferences and Beliefs Are Heterogeneous
Movements in asset prices are a major risk confronting individuals. This paper establishes new asset pricing results when agents differ in risk preference, time preference and/or expectations. It shows that risk tolerance is a critical concept driving savings decisions, consumption allocations, prices and return volatilities. Surprisingly, due to the equilibrium risk sharing, the precautionary savings motive in the aggregate can vastly exceed that of even the most prudent actual agent in the economy. Consequently, a low real interest rate, resulting from large aggregate savings, can prevail with reasonable risk aversions for all agents. One downside of a large aggregate savings motive is that savings rates become extremely sensitive to output fluctuation. Thus, the same mechanism that produces realistically low interest rates tends to make them unrealistically volatile. A powerful isomorphism allows differences in time preference and expectations to be swept away in the analysis, yielding an equivalent economy whose agents differ merely in risk aversion. These results hold great potential to simplify the analysis of heterogeneous-agent economies, as we demonstrate in quantifying how asset prices move and bounding their volatilities. All results are obtained in closed form for any number of agents possessing additively separable preferences in an endowment economy.
A framework for semiqualitative reasoning in engineering applications
In most cases the models for experimentation, analysis, or design in engineering applications
take into account only quantitative knowledge. Sometimes there is a qualitative knowledge
that is convenient to consider in order to obtain better conclusions. These qualitative concepts
can be labels such as ``high,’ ’ ``very negative,’ ’ ``little acid,’ ’ ``monotonically increasing’ ’
or
symbols such as ¾; º, etc. . . Engineers have already used this type of knowledge implicitly
in many activities. The framework that we present here lets us express explicitly this
knowledge.
This work makes the following contributions. First, we identify the most important classes
of qualitative concepts in engineering activities. Second, we present a novel methodology to
integrate both qualitative and quantitative knowledge. Third, we obtain signi®
cant conclusions automatically. It is named semiqualitative reasoning.
Qualitative concepts are represented by means of closed real intervals. This
approximation is accepted in the area of Arti® cial Intelligence. A modeling language
is speci® ed to represent qualitative and quantitative knowledge of the model. A
numeric constraint satisfaction problem is obtained by means of corresponding
rules of transformation of the semantics of this language. In order to obtain conclusions,
we have developed algorithms that treat the problem in a symbolic and numeric way. The
interval conclusions obtained are transformed into qualitative labels through a
linguistic interpretation. Finally, the capabilities of this methodology are illustrated on
different problems
Sobolev gradients and image interpolation
We present here a new image inpainting algorithm based on the Sobolev
gradient method in conjunction with the Navier-Stokes model. The original model
of Bertalmio et al is reformulated as a variational principle based on the
minimization of a well chosen functional by a steepest descent method. This
provides an alternative of the direct solving of a high-order partial
differential equation and, consequently, allows to avoid complicated numerical
schemes (min-mod limiters or anisotropic diffusion). We theoretically analyze
our algorithm in an infinite dimensional setting using an evolution equation
and obtain global existence and uniqueness results as well as the existence of
an -limit. Using a finite difference implementation, we demonstrate
using various examples that the Sobolev gradient flow, due to its smoothing and
preconditioning properties, is an effective tool for use in the image
inpainting problem
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