A framework is provided for pricing derivatives on defaultable bonds and other credit-risky contingent claims. The framework is in the spirit of reduced-form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. Although the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced-form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no-default version of the same claim, and recovery of a fraction of the pre-default value of the claim. A stochastic-integral representation for credit-risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity-based, reduced-form models, credit spread and credit-risky term structure are studied.

A number of recent cross-sectional studies of longevity and health among the elderly have concluded that recent positive trends in the prolongation of life have not been matched by similar trends in the extension of healthy life. This paper challenges that pessimistic conclusion by examining conceptual issues related to the measurement and dynamics of the mortality-disability process. It uses data from the 1986 Longitudinal Study of Aging (U.S. Department of Health and Human Services, 1988) to illustrate its principal points.

This paper provides a systematic, multidimensional demographic analysis of the degree to which negative economic consequences of population aging can be mitigated by changes in migration and labor-force participation. Using a microsimulation population projection model accounting for 13 individual characteristics including education and immigration-related variables, we built scenarios of future changes in labor-force participation, migration volumes, and their educational composition and speed of integration for the 28 European Union (EU) member states. We study the consequences in terms of the conventional age-dependency ratio, the labor-force dependency ratio, and the productivity-weighted labor-force dependency ratio using education as a proxy of productivity, which accounts for the fact that not all individuals are equality productive in society. The results show that in terms of the more sophisticated ratios, population aging looks less daunting than when only considering age structure. In terms of policy options, lifting labor-force participation among the general population as in Sweden, and education-selective migration if accompanied by high integration, could even improve economic dependency. On the other hand, high immigration volumes combined with both low education and integration leads to increasing economic dependency. This shows the high stakes involved with integration outcomes under high migration volumes.