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Δελτίο Τύπου
Συνέδριο Γενεύης
20-22 Απριλίου 2007
Ο καθηγητής Ιωάννης Κ. Δημητρίου ως μέλος της επιστημονικής επιτροπής
του International Workshop on Computational and Financial Econometrics
που διεξήχθη στο Πανεπιστήμιο της Γενεύης, 20-22 Απριλίου 2007, οργάνωσε
τη συνεδρία «Time series smoothing and modeling». Ερευνητικές εργασίες
παρουσίασαν ο Ι.Δ. (Separation of extrema of piecewise monotonic time
series), η υποψήφια διδάκτωρ Σοφία Σταυράκη (A control systems approach
for credit risk simulation and control of a loan portfolio, από κοινού
με το Λέκτορα Ι. Λεβεντίδη και τον κ. Χ. Πανδή), ο ΥΔ Ευάγγελος
Βασιλείου (A distributed lag estimator derived from smoothness priors
and nonnegative divided differences) και ο ΥΔ Σωτήριος Παπακωνσταντίνου
(Νecessary and sufficient conditions for a best L1 convex fit to
univariate data). Οι περιλήψεις των εργασιών μπορούν να βρεθούν στην
ιστοδιεύθυνση
it.econ.uoa.gr. Το πλήρες πρόγραμμα του συνεδρίου βρίσκεται στη
διεύθυνση
www.csdassn.org/europe/ CFE07/.
SEPARATION OF EXTREMA OF PIECEWISE MONOTONIC TIME SERIES
Abstract If time
series data include uncorrelated errors, then piecewise monotonic trends
in time series may be captured by a least squares fit to the data so
that the sequence of the first differences of the components of the fit
includes at most k-1 sign changes. The best fit is composed of at most k
monotonic sections, alternately increasing and decreasing, whereas the
positions of its extrema are integer variables of the optimization
calculation. We prove that as the time series data increase, the
positions of the corresponding extrema of the best fit increase as well.
One strong corollary is that the local maxima of a best fit with k-1
monotonic sections are separated by the local maxima of the best fit
with k monotonic sections, and local minima separate similarly.
Interesting applications of these results may be found in local
analyses, in extrema forecasting concerning future events of the time
series and in developing fast procedures for smoothing the time series.
A
DISTRIBUTED LAG ESTIMATOR DERIVED FROM SMOOTHNESS PRIORS AND NONNEGATIVE
DIVIDED DIFFERENCES
Ε. E.
Vassiliou (evagvasil@econ.uoa.gr)
Abstract We consider
noisy measurements from a time series that follow a linearly distributed
lag model. It is usual to assume that the lag coefficients lie on some
curve and then specify the curve by a least squares calculation.
However, we define the r-th order smoothness priors by requiring
nonnegative divided differences of order r for the lag coefficients.
Such priors do not imply any parameterization of the lag curve and
provide a more accurate representation of the prior knowledge. For the
calculation of the solution we propose an algorithm that gives the least
squares change to the data subject to nonnegative divided differences of
the lag coefficients of order r, where r is a prescribed positive
integer. The problem is a strictly convex quadratic programming
calculation, where each of the constraints functions depends on r+1
adjacent components of the smoothed values of the lag coefficients. We
take account of this special structure and use a special active set
method that is more efficient than general quadratic programming
algorithms. In fact we construct a basis that reduces the
equality-constrained minimization calculation to an unconstrained
minimization one, which depends on much fewer variables.
NECESSARY AND SUFFICIENT CONDITIONS FOR A
BEST
L1 CONVEX FIT TO UNIVARIATE DATA
Abstract If
plotted values of measurements of function values show some gross errors
and away from them the function seems to be convex, then it is suitable
to make the least sum of absolute change to the data subject to the
condition that the second divided differences of the smoothed data are
nonnegative. Note that: (1) it is a constrained L1 approximation
problem, which can be expressed as a linear programming calculation, (2)
the constraints enter by the assumption of non-decreasing returns of the
underlying function, which implies convexity, (2) the piecewise linear
interpolant to the smoothed data is a convex curve, (4) the
corresponding least squares and minimax problems have been characterized
long ago, and (5) convexity is a property that occurs in several
disciplines, as, for example, in estimating a utility function that is
represented by a finite number of observations that are corrupted by
random errors. Necessary and sufficient conditions for a solution to
this L1 problem are presented that allow the development of a special
algorithm that is much faster than general linear programming
procedures.
A
CONTROL SYSTEMS APPROACH FOR CREDIT RISK SIMULATION AND CONTROL OF A
LOAN PORTFOLIO
J.Leventides,
S. Stavraki & H. Pandis (ylevent@econ.uoa.gr,
sstavrak@econ.uoa.gr)
Abstract In this
paper, we study the problem of measurement and control of credit risk in
a loan portfolio. We develop a control systems methodology in order to
examine the dynamic behavior of a loan portfolio by modeling it as a
dynamical system which in turn is used for the definition of an
appropriate Optimal Control problem. In fact, we develop two discrete
dynamical systems, which describe the process and the evolution of the
loan portfolio by following two different approaches.
First we construct a
linear time invariant discrete system in state space form, where the
state variables are the amount of current loans, the amount of past due
loans and the amount of bad credit loans. The input of the system is the
amount of new loans. The coefficients of the system reflect the credit
quality, the repayment of due loans, the recoveries of bad credit and
the percentage of repayment of current loans. The construction of the
dynamical model is based on the historical data. For the identification
of this system, using monthly data for the variables, we solve an error
minimization problem with respect to the parameters of the system.
Subsequently, we examine the stability and the step response of the
system and, by simulating the system; we compute basic indices of the
loan portfolio for every time period.
Secondly we enhance the
above mentioned approach by using a refined set of variables reflecting
the variety of risk categories in the loan portfolio. The dynamical
system includes seven risk categories and the parameters of the
transitions between them. The inputs of the system are the new loans for
each risk category whereas the outputs are the various quality
parameters of the loan portfolio such as bad loans ratio, profitability
vs. risk etc. This approach may lead to portfolio planning and budgeting
either through simulations of the above dynamic model or via
determination of an open or closed loop policy using some optimality
criterion.
According to our approach we define an optimal
control problem of maximizing the profit of the portfolio under the
constraints of the equations of the dynamical system and an additional
inequality for restraining the risk of the portfolio. This problem is
proved to be equivalent to a linear programming problem and its solution
may lead to an optimal closed or open loop policy. This policy may be
interpreted as the optimal distribution of new loans for each risk
category that maximizes profit of the portfolio keeping in the same time
credit risk within acceptable limits.
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