Dynamically complete markets under Brownian motion

Abstract This paper investigates how continuous-time trading renders complete a financial market in which the underlying risk process is Brownian motion. A sufficient condition, that instantaneous dispersion matrix of relative dividends non-degenerate, has been established literature for single-commodity, pure-exchange economies with many heterogenous agents where securities’ as well agents’ utilities and endowments include flows during horizon are analytic functions. In sharp contrast, present analysis based upon different mathematical argument assumes neither analyticity nor particular economic environment. The novelty our approach lies deriving closed-form expressions coefficients prices. To this end, we assume only pricing kernels satisfy standard growth smoothness restrictions (mild enough to allow even options). sense, sufficiency conditions apply irrespectively preferences, or other structural elements (for instance, whether not budget constraints pure exchange).