| Abstract [eng] |
The research subject of the dissertation is the analysis of the model of heterogenous agents and its application for modelling stochastic Nash and Stackelberg equilibriums, applying the Monte Carlo method. The aim of the dissertation is to identify the impact of heterogeneous agents on the formation of the economic bubble, to create and examine algorithms for special bilevel stochastic programming problems and for search of the stochastic Nash equilibrium, applying the Monte Carlo method. The thesis offers a mathematical model for identification of the beginning of the bubble. This model has been applied for the analysis of the real estate bubble in Lithuania. In cases of uncertainty, decisions are often made by several individuals whose interests do not coincide. In such situations one of the concepts of the equilibrium is the stochastic Nash equilibrium. The dissertation examines the stochastic Nash equilibrium and offers the algorithm for gradient search of this equilibrium. The algorithm for gradient search of the stochastic Nash equilibrium was examined by solving the problem of electricity market with precedent agreements. The dissertation offers the algorithm for solving the optimization problem where the objective function and constraints contain conditional value at risk and by solving the test problem the behaviour of the algorithm is investigated. The dissertation proposes the algorithm for solving the two stage stochastic linear problem, employing the method of importance sampling, and demonstrates that this algorithm enables to reduce the number of iterations and the volume of Monte Carlo sample in each iteration, which is necessary for finding the solution with proper accuracy. |
