Sanov meets Cramér again

We introduce a new method for proving large-deviation principles (LDPs). This method amounts to "mixing" a collection of LDPs with a sequence of probability measures that obeys itself an LDP. As an illustration, we construct from empirical measures a sequence of capacity-valued maps that can be considered as an indexed collection of LDPs. The index 1 coincides with Sanov's theorem. By taking a Poisson mixture we establish a new connection with Cramér's theorem.     

Computing equilibria of GEI by relocalization on a Grassmann manifold

An algorithm is described to compute equilibria of the general economic model with incomplete asset markets, that is, of GEI. The algorithm is based on the existence of a route of zeros of a homotopy whose domain includes the price simplex and a Grassmann Manifold. This route is followed, in effect, by localizing and following diffeomorphic pieces in Euclidean space, and by relocalizing as is necessary.     

Bivariate and multivariate scaled association models. An application to homogamy of social origin and education in Hungary between 1930 and 1979

In this article we compare bivariate and multivariate models for homogamy of social origin and education to test whether bivariate models of homogamy lead to biased results. We use data on Hungarian couples married between 1930 and 1979 and loglinear models of scaled association. The results indicate some differences between bivariate and multivariate analyses. At each point of time bivariate models overestimate homogamy, both with respect to education and social origin. However, results on trends in time do not differ much between the two analyses. The exception is the period 1940–1959, in which bivariate analysis showed decreasing educational homogamy, and multivariate analysis showed an increasing trend. The latter finding can be explained by declining homogamy of social origin, as well as the weaker reproduction and cross-effects in this period.     

Choice of utility function form: its effect on classification of risk preferences and the prediction of farmer decisions

In applications of expected utility analysis, researchers are confronted with a choice among several utility functional forms. Subjective utility values and probability distributions for price and yield were elicited from Sri Lankan producers of minor export crops. Exponential quadratic and cubic utility functions were estimated. The choice of functional form was found to affect both the classification of risk attitudes and the prediction of harvesting strategy. The exponential function was the best predictor of harvesting strategy because it was the best predictor of mature harvesting. All three functions were equally poor predictors of premature harvesting.     

Pricing Options on an Asset with Bernoulli Jump-Diffusion Returns

The price movements of certain assets can be modeled by stochastic processes that combine continuous diffusion with discrete jumps. This paper compares values of options on assets with no jumps, jumps of fixed size, and jumps drawn from a lognormal distribution. It is shown that not only the magnitude but also the direction of the mispricing of the Black-Scholes model relative to jump models can vary with the distribution family of the jump component. This paper also discusses a methodology for the numerical valuation, via a backward induction algorithm, of American options on a jump-diffusion asset whose early exercise may be profitable. These cannot, in general, be accurately priced using analytic models. The procedure has the further advantage of being easily adaptable to nonanalytic, empirical distributions of period returns and to nonstationarity in the underlying diffusion process.