292,610 research outputs found
The risk of divergence
We present infinite extensive strategy profiles with perfect information and
we show that replacing finite by infinite changes the notions and the reasoning
tools. The presentation uses a formalism recently developed by logicians and
computer science theoreticians, called coinduction. This builds a bridge
between economic game theory and the most recent advance in theoretical
computer science and logic. The key result is that rational agents may have
strategy leading to divergence .Comment: 3rd International Workshop on Strategic Reasoning, Dec 2015, Oxford,
United Kingdom. 201
Robust Kalman Filtering under Model Perturbations
We consider a family of divergence-based minimax approaches to perform robust
filtering. The mismodeling budget, or tolerance, is specified at each time
increment of the model. More precisely, all possible model increments belong to
a ball which is formed by placing a bound on the Tau-divergence family between
the actual and the nominal model increment. Then, the robust filter is obtained
by minimizing the mean square error according to the least favorable model in
that ball. It turns out that the solution is a family of Kalman like filters.
Their gain matrix is updated according to a risk sensitive like iteration where
the risk sensitivity parameter is now time varying. As a consequence, we also
extend the risk sensitive filter to a family of risk sensitive like filters
according to the Tau-divergence family
Set-valued shortfall and divergence risk measures
Risk measures for multivariate financial positions are studied in a
utility-based framework. Under a certain incomplete preference relation,
shortfall and divergence risk measures are defined as the optimal values of
specific set minimization problems. The dual relationship between these two
classes of multivariate risk measures is constructed via a recent Lagrange
duality for set optimization. In particular, it is shown that a shortfall risk
measure can be written as an intersection over a family of divergence risk
measures indexed by a scalarization parameter. Examples include set-valued
versions of the entropic risk measure and the average value at risk. As a
second step, the minimization of these risk measures subject to trading
opportunities is studied in a general convex market in discrete time. The
optimal value of the minimization problem, called the market risk measure, is
also a set-valued risk measure. A dual representation for the market risk
measure that decomposes the effects of the original risk measure and the
frictions of the market is proved
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