Recursive valuation of defaultable securities and the timing of resolution of uncertainty

We derive the implications of default risk for valuation of securities in an abstract setting in which the fractional default recovery rate and the hazard rate for default may depend on the market value of the instrument itself, or on the market values of other instruments issued by the same entity (which are determined simultaneously). A key technique is the use of backward recursive stochastic integral equations. We characterize the dependence of the market value on the manner of resolution of uncertainty, and in particular give conditions for monotonicity of value with respect to the information filtration.