In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent." We...

We construct a financial market with countably many securities for which there are two equivalent martingale measures under which the market is approximately complete. Thus, approximate completeness does not in general guarantee unique consistent prices for nonmarketed claims. the construction...