APPLYING STOCHASTIC LINEAR PROGRAMMING FOR PORTFOLIO IMUNIZATION

V diplomskem delu je v začetnem delu predstavljeno linerano programiranje, ki se uporablja vsakodnevno pri optimizacijskih problemih. V nadaljevanju linearno programiranje obravnavamo stohastično, kar pomeni, da v problem vključimo faktor naključnosti. Pri tem reševanje linearnih programov ostaja prisotno, saj stohastične probleme preoblikujemo v deterministično obliko in rešujemo njegov deterministični ekvivalent, do katerega lahko pridemo po različnih poteh, glede na vrsto problema, ki ga rešujemo. Za reševanje stohastičnih problemov in na splošno optimizacijskih problemov se je na spletu oblikovalo veliko reševalcev, ki zahtevajo vhodne podatke v določenih formatih datotek. Zato sta v diplomskem delu opisana formata datotek MPS za zapis linearnega programa in SMPS za zapis stohastičnega linearnega problema, s pomočjo katerih opišemo določeni problem in ga posredujemo reševalcu, ki nam potem izpiše rešitev. V zadnjem delu pa je predstavljen model imunizacije portfelja, ki oblikuje strategijo strukturiranja portfelja, tako da se zavarujemo pred obrestnim tveganjem in je torej uporaben za vse finančne institucije, ki so izpostavljene obrestnemu tveganju. Delovanje modela je predstavljeno na konkretnih podatkih, rešitev pa poiskana s pomočjo Neos reševalca.At the beginning of this diploma we present linear programming, which is used daily in optimisation problems. We continue with presenting linear programs stochastically, by adding factor of randomnes in linear programming. As we do so, linear programming remains present, because we solve stochastical problems with transtorming them into detreministic equivalents. We can transform them with different methods, depending on what kind of problem are we dealing with. For solving stochastical problems and for all optimisation problems there are many solvers on the internet, which require input data in a specific form. That is why we present the formats MPS file, for linear programs and SMPS file, for stochastical programs, using them to describe the problem that we want to solve, and then we send the file to the solver on the inernet, which returns us the solution. In the last part, we present the model for portfolio immunization, which forms the strategy for structuring portfolio immune of interest rate. This model is usefull for every financial institution, which is exposed to interest rate risk. We describe the functioning of the model on real data and solve the problem with the help of solver