The main purpose of this paper is to provide a quantitative analysis to investigate the behavior of the OPEC oil price. Obtaining the best mathematical equation to describe the price and volatility of oil has a great importance. Stochastic differential equations are one of the best models to determine the oil price, because they include the random factor which can apply the effect of different ...

Markov-modulated processes have been used in stochastic inventory models with setup costs for modeling demand under the innuence of uncertain environmental factors, such as uctuating economic and market conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatissed demand is fully backlogged. The lost sales situation occurs in many ret...

A linear version of backward stochastic differential equations (BSDEs) was first studied by Bismut [4] as the adjoint processes in the maximum principal of stochastic control. Pardoux and Peng in [20] introduced the notion of nonlinear BSDE. Since then, the interest in BSDEs has increased. Indeed, BSDEs provide connection with mathematical finance [10], stochastic control [11], and stochastic g...

<p style='text-indent:20px;'>This paper is concerned with a linear quadratic stochastic Stackelberg differential game time delay. The model general, in which the state delay and control both appear equation, moreover, they enter into diffusion term. By introducing two Pseudo-Riccati equations special matrix feedback representation of open-loop strategy derived, under some assumptions. Fin...

We study a class of second order nonlinear variational inequalities with bilateral constraints. This type of inequalities arises in zero sum stochastic differential games of mixed type where each player uses both continuous control and stopping times. Under a nondegeneracy assumption Bensoussan and Friedman [1,4] have studied this type of problems. They proved the existence of a unique solution...

With the increasingly severe global warming, investments in clean technology, reforestation and political action have been studied to reduce CO2 emission. In this study, a nonlinear stochastic model is proposed to describe the dynamics of CO2 emission with control inputs: clean technology, reforestation and carbon tax, under stochastic uncertainties. For the efficient resources management, a ro...