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SUMMARY
The paper presents stochastic optimisation approach to strategic public debt
management with an example of application to Polish case. Stochastic features appear in
many components of debt management process, especially forecasts of interest rates and
budgetary requirements level. Stochastic character of interest rates forecasts can be taken into
account in constraints of risk level, e.g. quadric of variance and covariance matrix. The
constraints of budgetary requirements needs another approach. They are of special
importance, because their variation is typically significant and can influence in unexpected
way the form of optimal solution. The spectrum of stochastic approaches (tasks) applicable in
such case is quite extensive. However, practical matters, e.g. computation time, possibility of
estimation of necessary parameters (random variables distributions), etc. impose significant
limitations in this area. Therefore, it has been implemented the method, which reflects the
basic features of decision making realities. Such criteria satisfies so called Dantzig-Madansky
approach. In this approach the parameter (vector) determining the constraint (its right-hand
side) is the multivariate random variable with known distribution. The case, when the
constraint is not satisfy as equality indicates surplus or shortage, that implies some costs; the
expected value of these costs is incorporated into criterion function. The surplus or shortage
are taken into account also in the form of constraints set. Solving of such task is more
difficult, than its deterministic version, but allows to capture more general case.
The approach was applied to optimisation of three-years debt management strategy in
Poland. The numerical form of the task needs prediction some number of quantities,
especially the functions expressing profitability of debt instruments (assumed in the form of
compound rate of return - CRR) for the strategy period. Prediction of these functions is not a
trivial problem. In earlier papers of authors some aggregated approach was applied for this
purpose (all bids from auctions from a whole year were considered as result of one auction).
This approach may be applied only in some circumstances, especially when interest rates are
stable in estimation period and optimisation horizon (may be not valid currently). Therefore,
it requires improvement. This approach is replaced in the paper with the prediction method
based on identification of typical features (shape) of CRR function. This identification is
performed with the use of classification algorithms; two algorithms have been examined 
first one based on pairwise comparisons and the second  on artificial neuronal networks. The
results of predictions seems satisfactory, but do not exhaust all possible approaches.
The numerical form of the optimisation task has been solved with the use of solver
package from Excel worksheet. The task comprise 30 decision variables and more than 50
29
constraints; discrete form of original task has been replaced with it continuous polynomial
approximation. The computation time does not exceed typically one minute (PC computer),
however sometimes many starting points had to be used. Apart optimal solution, some
number of sub-optimal solutions have been obtained with values of the criterion function
close to optimal, but with different values of decision variables. These differences influence
significantly some properties of the solutions (debt issued), e.g. risk parameters. It indicates,
that there exist some number of solutions which generate similar servicing costs with different
maturity distribution, duration, etc. It is not surprising, because discrete problems can have
many optimal solutions (the task is continuous approximation of the discrete problem).
Implementation of optimisation approach emphasizes also the components of decision
process which are leaved out in debt management based on intuition and experience only.
Moreover, it increases transparency of assumptions and results and allows complex
automation of computations. As a result it provides optimality of results, reduction of labour
costs and computations time. Therefore, it seems obvious, that traditional approach based on
intuition and experience should become a history.
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Treść pracy zawiera poglądy autorów  nie wyraża stanowiska Departamentu Długu
Publicznego Ministerstwa Finansów, w którym są zatrudnieni.
Autorzy:
Leszek Klukowski, Elżbieta Kuba
Departament Długu Publicznego Ministerstwa Finansów
Tel. 694 42 20
e-mail: lkl@mofnet.gov.pl , Kuba Elżbieta@mofnet.gov.pl
fax: 827 27 21 .
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