A DISCRETE-TIME EQUIVALENT MARTINGALE MEASURE

An equivalent martingale measure selection strategy for discrete time, continuous state, asset price evolution models is proposed. The minim al martingale law is shown to generally fail to produce a probability law in this context. The proposed strategy, termed the extended Girsan ov principle, performs a multiplicative decomposition of asset price m ovements into a predictable and martingale component with the measure change identifying the discounted asset price process to the martingal e component. However, unlike the minimal martingale law, the resulting martingale law of the extended Girsanov principle leads to weak form efficient price processes. It is shown that the proposed measure chang e is relevant for economies in which investors adopt hedging strategie s that minimize the variance of a risk adjusted discounted cost of hed ging that uses risk adjusted asset prices in calculating hedging retur ns. Risk adjusted prices deflate asset prices by the asset's excess re turn. The explicit form of the change of measure density leads to trac table econometric strategies for testing the validity of the extended Girsanov principle. A number of interesting applications of the extend ed Girsanov principle are also developed.