Kind Of Multi-asset Option Problems

Real option is a very hot topic presently. As a typical problem (the investment problem of some factory), the paper talks the real option problem about multi-dimension assets.In the preface, we introduce the background of real option, present condition of studying of option problems about real assets and what we are going to do in the paper.In chapter 1, we introduce some important conclusions that will be used in the paper about stochastic differential equation (SDE) and stochastic control, such as Ito formula, Hamilton-Jacob!-Bellman (HJB) equation.In chapter 2, using correlated conclusions of the optimal control, we formulate a stochastic control model about the optimal producing scheme, which includes a state equation, a payoff equation and so on. Where commodity prices satisfy a SDE and the payoff function is a general payoff function with stopping time.In chapter 3, using dynamic programming and the theory of optimal stopping, we determine a HJB equation that the value function satisfy, while we prove a general existence result about the optimal strategy.In chapter 4, we study a partial differential equation (PDE) corresponding to chapter 3, and talk the construction and certain properties of a special solution of the PDE that we have had. Where we consider correlated conclusions under a special case (the producing of commodities is independent).In chapter 5, we explicitly solve the HJB equation that is derived in chapter 4 and get an optimal strategy about the producing and stopping time.In chapter 6, we explain some special case (the running payoff function is linear expression of commodity prices.), where involve several parameters. The analysis results in closed form analytic solutions that can easily be computed and exhibits qualitatively different optimal behaviors, depending on parameter values.In chapter 7, we summarize the paper and put forward the possible trainof thought of further studying.