Numerical Valuation of High Dimensional Multivariate American Securities
研究如何对依赖多个风险源的美式或有权益进行定价，指出传统方法（如格点法和有限差分法）因内存需求随风险源数量指数增长而无法处理高维问题。
We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty.Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted expected cash flows under the modified risk-neutral information process.Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources.They are either lattice-based techniques or finite difference approximations of the Black-Scholes diffusion equation.However, these methods cannot be used for high-dimensional problems, since their memory requirement is exponential in the number of risk sources.