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.     

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.