Two Families of Theta Milstein Methods in A Real Options Framework

DOI: 10.5176/2251-1911_CMCGS16.3

Authors: Boping Tian, Mahmoud A. Eissa and Shijie Zhang

Abstract: This paper presents a new split-step meth- ods for solving It^o stochastic di erential equations (SDEs) and its applicability for real option valuation problems. Two families of methods, a family of drift- ing split-step Theta Milstein (DSSM) methods and modi ed split-step Theta Milstein (MSSM) methods are constructed. Strong convergence with order 1.0 and mean-square (MS) stability of MSSM methods are established. Satellite missions are facing uncer- tain return streams and high sunk cost. So, A real option framework for use in space mission planning is presented. A new split-step methods are integrated with concepts of Black-Scholes option pricing theory and economic principles of cost, value, risk and exi- bility. This paper provides real option valuation frame- work for information is obtained from Earth observa- tion which can be used to mitigate the damage from disasters. Also, optimize the timing of the launch of a satellite mission to maximizing mission utility is dis- cussed. Ex ante expected value bene t assessment of information is an important approach.

Keywords: Real option, Satellite missions planning, Stochastic di erential equation, Mean square stability, Convergence, Split step Theta Milstein methods