This paper uses the existence of secondary markets for debt instruments with default risk (e.g. corporate bonds) to define default insurance along the lines of financial economics. It examines whether, in the case of several risk-neutral measures, characteristics of default can be uniquely...

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...

We give two examples showing that for unbounded continuous price processes, the no-free-lunch assumption and the existence of an equivalent martingale measure are not equivalent. In fact it turns out that the notion of an equivalent local martingale measure is natural in this context. Copyright...

We relate the theory of passport options with general principles from martingale theory as well as with the theory of Bessel processcs. The calculation of the price of a passport option leads to an equality between two norms on continuous martingales. We also solve the discrete time case for...

We give an easy example of two strictly positive local martingales that fail to be uniformly integrable, but such that their product is a uniformly integrable martingale. The example simplifies an earlier example given by the second author. We give applications in mathematical finance and we...