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its extensions. Annals of Operations Research vol. 51. Klukowski L. (1998) Problemy optymalizacji zarządzania zadłużeniem budżetu państwa w Polsce. Nasze Finanse nr 26, marzec kwiecień, Wyd. Biura Prasowego Ministerstwa Finansów. 27 Klukowski L. (2000) Sformułowanie zadań optymalizacyjnych dla minimalizacji kosztów obsługi skarbowych instrumentów dłużnych. Bank i Kredyt nr 3, NBP. Klukowski L. (w przygotowaniu) Optymalizacja zarządzania instrumentami dłużnymi Skarbu Państwa. Klukowski L., Kuba E. (2001a) Optymalizacja zarządzania długiem Skarbu Państwa. Minimalizacja kosztów obsługi instrumentów dłużnych emitowanych na rynku krajowym. NBP Materiały i Studia, zeszyt 119. Klukowski L., Kuba E. (2001b) Minimization of public debt servicing costs based on nonlinear mathematical programming approach. Control and Cybernetics, vol. 30, no 1. IBS PAN. Klukowski L., Kuba E. (2002) Optymalizacja zarządzania długiem Skarbu Państwa w horyzoncie trzyletnim. W: Kacprzyk J., Węglarz J. (red.) Badania Operacyjne i Systemowe wobec wyzwań XXI wieku. Modelowanie i optymalizacja, metody i zastosowania. Akademicka Oficyna Wydawnicza EXIT, Warszawa. Referat wygłoszony na VII Konferencji Polskiego Towarzystwa Badań Operacyjnych i Systemowych BOS 2002, zorganizowanej w Warszawie, w dn. 26 28.09.2002 r. Osowski S. (1996) Sieci neuronowe w ujęciu algorytmicznym. WNT, Warszawa (wyd. drugie). 28 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. 30 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 . 31 [ Pobierz całość w formacie PDF ] |