Some numerical methods for solving stochastic impulse control in natural gas storage facilities

The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP

Analytical development and optimization of a graphene-solution interface capacitance model

Graphene, which as a new carbon material shows great potential for a range of applications because of its exceptional electronic and mechanical properties, becomes a matter of attention in these years. The use of graphene in nanoscale devices plays an important role in achieving more accurate and faster devices. Although there are lots of experimental studies in this area, there is a lack of analytical models. Quantum capacitance as one of the important properties of field effect transistors (FETs) is in our focus. The quantum capacitance of electrolyte-gated transistors (EGFETs) along with a relevant equivalent circuit is suggested in terms of Fermi velocity, carrier density, and fundamental physical quantities. The analytical model is compared with the experimental data and the mean absolute percentage error (MAPE) is calculated to be 11.82. In order to decrease the error, a new function of E composed of α and β parameters is suggested. In another attempt, the ant colony optimization (ACO) algorithm is implemented for optimization and development of an analytical model to obtain a more accurate capacitance model. To further confirm this viewpoint, based on the given results, the accuracy of the optimized model is more than 97% which is in an acceptable range of accurac

Natural Gas Storage Valuation Based on Observable Gas Prices

This study aims to formulate and solve the natural gas storage facility valuation problem by emphasizing the impact of observable gas prices on storage operational policies. In a deregulated market, non-energy players could enter the market and rent the storage facilities. As market prices of gas are revealed, the leaseholders dynamically adjust their operational decision to derive the maximum benefit from the price fluctuation. However, the direct influence of available gas prices on storage values has been neglected in the literature. The current work derives the market filtration based on observable asset prices, and formulates the storage problem within the Brody-Hughston-Macrina (BHM) X-factor pricing theory to fill the gap in the literature. The essence of this research is to use the stochastic dynamics of price revelation in back-testing procedure rather than to calibrate the spot and forward prices. This effort theoretically contributes to improve the BHM pricing framework for randomly timed cash-flow assets and to construct the market filtration and σ-algebra incorporating two uncertainty sources of price fluctuation and random switch times. Thereafter, a numerical scheme is developed based on Monte Carlo regression to solve the corresponding optimal switching problem. Then, this Least Square Monte Carlo (LSM) technique is extended to the Info-LSM method in order to back-test the resulted strategy on the available information. The designed decision-making algorithms are efficient because they possess polynomial time and memory complexities. In terms of performance, the developed LSM algorithm reduces the total execution time by approximately 50%, especially in the case of a storage problem with a linear ordinary differential equation inventory level. Moreover, the experiments depict the empirical convergence of both schemes to the exact solutions with smaller standard deviations. Furthermore, the extended technique provides a very short list of the admissible strategies and indicates that the majority of simulated strategies are not acceptable, subject to the current market situations. In conclusion, this study enables decision-makers to solve the switching problems and back-test the solution on the observable asset prices without using any financial instruments

Modeling of information flows in natural gas storage facility

The paper considers the natural-gas storage valuation based on the information-based pricing framework of Brody-Hughston-Macrina (BHM). As opposed to many studies which the associated filtration is considered pre-specified, this work tries to construct the filtration in terms of the information provided to the market. The value of the storage is given by the sum of the discounted expectations of the cash flows under risk-neutral measure, conditional to the constructed filtration with the Brownian bridge noise term. In order to model the flow of information about the cash flows, we assume the existence of a fixed pricing kernel with liquid, homogenous and incomplete market without arbitrage