Given a finite collection of continuous semimartingales, we derive a semimartingale decomposition of the corresponding ranked (order-statistics) processes. We apply the decomposition to extend the theory of equity portfolios generated by ranked market weights to the case where the stock values...

We derive the decomposition of the ranked continuous semimartingales i.e. order-statistics processes. We apply it to portfolios generated by functions of the ranked market weights. Thus we generalize recent results of Fernholz.

In this note we extend and clarify some identities in law for Brownian motion proved by Seshadri (Canad. J. Statist. 16 (1988) 209) using a new identity in law obtained by Matsumoto and Yor (Proc. Japan Acad. Ser. A Math. Sci. 74 (1998) 152).