A 3D Numerical Model of Mine Value Stochastic Processes Using Dynamic Arbitrage Theory

Superior ventures selection and the subsequent management of their development and production are crucial in the competitive environment of the upstream minerals and energy industry. An important element of this chain is the management of uncertainty and risk dynamics. In the world of faster and more complicated technological and environmental changes, international competition and commodity market dynamics, thorough and sophisticated valuation must be carried out to establish a venture's value and return on investment. Thus, managers and investors must use methods that respond to market dynamics, investment and feasibility study options and provide relevant information for strategic investment decisions. Conventional methods have no built-in procedures to help investors analyse these options. Modern financial methods based on the dynamic arbitrage theory overcome these and other limitations of conventional methods. In this study, dynamic arbitrage theory has been used to formulate 3D parabolic differential equations that govern the stochastic processes of a copper mining venture with ongoing feasibility studies. The alternate direction implicit algorithm is used to solve the numerical approximations of the differential equations and their boundary conditions. Phase dynamics of the venture have been analysed to provide investors the appropriate timing for strategic investment decisions. The study also shows the amount and value of appropriate feasibility studies required to maximize the value of the mining venture.