Abstract
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).
Highlights
In the natural gas industry, the modelling and valuation of leases on natural gas storage have been major concerns in the last decade, especially since deregulation of U.S and Europe energy markets
Since the optimal switching is a special case of impulse control, one can use the classical methods of solving stochastic impulse control problems which relates to studying the parabolic partial differential equations (PDEs) resulted from applying Bellman’s optimal principle
The PDE methods transform the stochastic control problem into a parabolic partial differential equation with a free boundary. To solve this parabolic PDE, there are a variety of tools such as the basic finite difference scheme (FD)
Summary
In the natural gas industry, the modelling and valuation of leases on natural gas storage have been major concerns in the last decade, especially since deregulation of U.S and Europe energy markets. The value of a gas storage contract can be computed by solving the corresponding HJB equation using partial differential equation (PDE)-based approaches such as typically finite difference (FD) methods. Besides the capability of handling multi-dimensional problems, this scheme considers the operational constraints in the model This simulation based methods [3, 11] can be used directly to solve the stochastic control problem with bang-bang type control. Such trees are just explicit finite difference methods for solving parabolic PDEs. In the case of natural gas storage the operating characteristics lead to equations of a parabolic and hyperbolic nature. The type of entity that owns/operates the facility will determine to some extent how that facility's storage capacity is utilized
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