In this paper, we discuss the pricing of stock index options. Under a generalized assumption that the underlying individual stock price which is an element of the stock index follows a semi-martingale process with correrlation, we derive the partial differential equation which the corresponding European stock index option prices satisfy. More precisely, we calculate the respective equilibrium prices for the value line index (VLI) option and the average stock index (ASI) option analytically and numerically. Finally, we perform the sensitivity analysis of model parameters in the option prices and the position analysis. Throughout numerical examples, it is shown quantitatively that the correlation for underlying assets is one of the most important factors to price stock index options.
The descriptor form provides system representations that preserve structure of systems along with static constraints on descriptor variables. Based on the descriptor-form representations of LPV (linear parameter varying) -systems, this paper proposes an approach to gain-scheduling controller synthesis. First, we show a descriptor form with scheduling parameters on the coefficient matrices and discuss using it as a model of LPV-systems. Next, we give a synthesis method of quadratically stabilizing LPV-controllers via solving LMIs for both state-feedback and output-feedback systems.
We have concerned, in this paper, with developing a practical method for multi-objective mixed-integer programming problems. To cope with the problem in the hierarchical framework, we have already proposed the hybrid genetic algorithm incorporated with a modeling method of a value function using neural networks. In its master problem, genetic algorithm will solve the unconstrained discrete optimization using the neural network model of the value function, and mathematical program will solve the slave problem given as the constrained continuous optimization. Due to such good matches between the solution methods and the problem properties, the hybrid strategy can derive the best-compromise solution very effectively while the so far methods were limited to derive the Pareto optimal solution set. Furthermore, we have proposed a repair operation of genetic algorithm which models the mechanism of DNA in nature. It enables us to reduce the search space in genetic algorithm and the derived best-compromise solution to be a Pareto optimal solution. Hence, we can improve both the efficiency and the reliability in solution much more compared with the foregoing method. To examine effectiveness of the proposed method in an actual application, we have concerned with a site location problems of hazardous wastes disposal. As known from the term NIMBY (Not In My Back Yard), it is an eligible case study associated both with environmental and economic concerns. After describing the problem generally as a multi-objective mixed-integer linear program, through numerical experiments, we have confirmed the proposed method can derive the best-compromise solution effectively. In addition, we have shown the repair operation of genetic algorithm can work better compared with a penalty function approach against the inactive ε-constraints and the foregoing method paying no concern on it.
A calculation method of Hankel singular values is discussed for input and unilateral time delay systems. For input time delay systems, whose channels involve different value of time delays independently, the Hankel singular values are obtained based on a matrix Lyapunov equation. By introducing auxiliary systems for the unilateral time delay system, it is shown that the singular values are characterized based on the preliminary results for input time delay systems. When Hankel singular values and vectors are derived for input and unilateral time delay systems, the calculation method of balanced reduction is constructed. We investigate balanced reduction with numerical examples.
Multi-story mechanical parking facilities are becoming popular in crowded cities, as they are space efficient. Each floor of such a facility consists of two rail-mounted automated carriers on a pair of rails running from one end to the other, and rows of cells along the rails, where each cell can accommodate one car. The number of rows varies from one to four. There are two elevators connecting all floors, which are dedicated to removal and placing of the cars, respectively. When many cars are waiting to enter and to leave, it is important to schedule the movement of carriers so that the required time is minimized. As a basic subproblem for an efficient scheduling of the total system, we consider here the problem of finding an optimal schedule when an ordered set of car removals is given. We present here an exact algorithm based on dynamic programming, which shows the problem can be solved in polynomial time even if it is a quite complicated combinatorial problem. Some computational results of nontrivial sizes are presented.
This paper describes a method for knowledge sharing in a community using associative representation. We propose two ideas. One is associative representation for facilitating externalization of both personal and community information. The associative representation links heterogenenous information without definding the semantics strictly. We leave the interpretation of the semantics to human tacit knowledge. The other is visualization of information interaction using talking-agents metaphor. Taking-agents metaphor mimics a salon in which agents representing each community member interact with each others, thereby the user can see how their own or others' knowledge interact. We have developed a system called CoMeMo-Community that pursues collaborative story generation based on the talking-agents metaphor. We investigated how far people can exchange ideas with associative representation and how people react the talking-agents metaphor.
This paper considers switching state feedback control of systems with unknown but bounded disturbance inputs subject to state and control constraints, and resolves convergence problems which arise with the effects of unknown disturbances. This difficulties have not been handled by the switching control laws which were proposed in the literatures. The proposed switching control law assures convergence of the state and successive controller switching even in the presence of unknown disturbances. The main idea is to construct an upper bound of the state reachable set ' such that convergence of the state is assured by restricting this set to some subset of the state space. The resulting optimization problems which provide a sequence of feedback gains are more difficult to solve than those with no disturbances. However, this optimization problems may be solved with some heuristic manners. In addition, required on-line computational burden is the same as that in case of no disturbance inputs.