The control problem and Dynamic programming is a powerful tool in economics and management. We review the dynamic programming problem from its beginning up to its present stages. A problem which was involved in physics and mathematics in I 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

The main aim of this work is to give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare [12]. In this approach, the semantics of a process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a compositional, finitely branching labelled transition system for Brane Calculus; interestingly, the assoc...

We propose an extension with immediate multiactions of discrete time stochastic Petri Box Calculus (dtsPBC), presented by I.V. Tarasyuk. The resulting algebra dtsiPBC is a discrete time analogue of stochastic Petri Box Calculus (sPBC) with immediate multiactions, designed by H. Macià, V. Valero et al. within a continuous time domain. The step operational semantics is constructed via labeled pro...

In this paper, we deal with the problem of implementing an abstract machine for a stochastic version of the Brane Calculus. Instead of defining an ad hoc abstract machine, we consider the generic stochastic abstract machine introduced by Lakin, Paulevé and Phillips. The nested structure of membranes is flattened into a set of species where the hierarchical structure is represented by means of n...

Branch and bound method and Pijavskii's method are extended for solution of global stochastic optimization problems. These extensions employ a concept of stochastic tangent minorants and majorants of the integrand function as a source of global information on the objective function. A calculus of stochastic tangent minorants is developed.

In this paper, performance evaluation of a cognitive radio network is conducted. The analysis is based on stochastic network calculus. The system is supposed to work in a Time Division Multiple Access (TDMA) mode with fixed slot length. The wireless channel is modeled as a Gilbert-Elliott (GE) fading channel, where the channel quality transits between state ON and state OFF according to a Marko...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin weights are effectively applied. We provide an expansion formula for generalized Wiener functionals a...