The Intelligent Transportation System (ITS) is used as a term for integrating requirements and functionalities towards transportation systems, which in urban environment raises complex exploitation and control problems. Important part of the ITS is the control which has to be applied for traffic flows. The control processes are strongly linked with requirements and targets for optimization of the transportation behavior. The paper applies new optimization formal description of control by bi-level optimization. Except the trivial traffic lights control, the bi-level formalization allows additional traffic characteristics to be defined like maximal/minimal values. The paper defines, solves and provides numerical simulations for minimization of the vehicle queues in front of the traffic lights. Such bi-level optimization problem is applied simultaneously for maximization the traffic flows on arterial and important directions of the urban transportation network. The formal description of the bi-level problem is provided. The results of the bi-level control have been compared with the cases of single optimization of the vehicles queues. The simulation results prove that the bi-level problem gives benefits satisfying an additional goal, which improves additional characteristic of the transport behavior. The bi-level optimization formalism can be used as a tool for implementation of integration of ITS control policies.

A bi-level model for traffic signal optimization is developed. The model predictive framework is applied for traffic control in an urban traffic network. The potential of the bi-level formalization is used to increase the space of control influences with simultaneous evaluation of the green light and cycle durations. Thus, the increased control space allows more traffic parameters to be considered, such as vehicles queues and traffic flows. A particular modification of the bi-level control is applied for the synchronization of the traffic lights in the network. The model predictive approach is used for the real-time management of the traffic in the network. The control implementations are constrained by the shortest evaluated cycle. Thus, a synchronization of the traffic lights is applied for the minimization of the queues and maximization of the outgoing flows from the network. The bi-level model has been numerically tested on a set of intensive crossroads in Sofia. The numerical simulations prove the superiority of the developed bi-level control in comparison with the classical optimization of queue lengths.

The paper makes analytical overviews of the Markowitz portfolio and the Capital Asset Pricing models and motivates the advances of the Black-Litterman (BL) one. This overview implies that for a small set of assets the BL model needs the characteristics of a specific market point, which cannot be taken from a global market index. The paper derives analytic relations for the new specific market point with analytical approximation of the efficient frontier. The BL model insists also expert views, which influence the portfolio solution. The paper derives formalization of the expert views from the difference between the evaluated implied returns and historical mean assets returns. Such form of expert views makes modifications of the BL model. This allows comparisons between Markowitz (MV) and BL portfolio performance. Benefits of this research are demonstrated with market data and comparison of the MV and BL portfolio results.

The general contribution of this research is the implementation of new formal type of relative view, which has been added to the Black-Litterman Model (BLM) for asset management. It is well known that the BLM integrates both historical data about the assets’ returns and subjective views given by experts and investors. Such complicated model is expected to give more realistic assessment about the dynamical behavior of the stock exchanges. The BLM applies both absolute and relative views about the asset returns. The paper proves that the currently applied relative views with equal weights are equivalent to assess the risk of a virtual portfolio with these assets of the view which participate with equal weights. The paper extends this form of views, applying non-equal weights of the assets. This new formal description has been tested on a market, containing ten world known indices for a 10 years period. The calculations which have been provided give benefits to the suggested non-equal weighted form of subjective views. It gives more conservative results and decreases the portfolio risk supporting the same level of returns, provided by the average market behavior.

An algorithm is derived for the development of portfolio decision-support information service. The algorithm allows being automated evaluations for the definition and solution of portfolio problems. Small set of historical data of asset returns with limited set of assets are used for the portfolio, which is the case for no institutional portfolio manager. The algorithm applies analytical relations for decreasing the computational workload for the estimation of the market parameters due to the limited number of assets. The subjective expert views in the Black–Litterman (BL) model are defined from additional assessment of historical data of the asset returns. The algorithm makes comparisons of the results for active portfolio management from the mean variance (MV) model, the BL one and the equal-weighted investment strategy. Benefits of the algorithm are the usage of small set of historical data and limited number of assets, which are proved in investment rolling horizon.