Hedging by sequential regressions revisited

Almost 20 years ago Föllmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of local risk minimization results in a sequence of one-period least squares regressions running recursively backwards in time. In the meantime there have been significant developments in the global risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by Černý and Kallsen (2007). A number of illustrative numerical examples is given

Small deviation estimates for some additive processes

Abstract. We study the small deviation probabilities for real valued additive processes. This naturally leads to the small deviation for the corresponding range process. Our general results can be applied to a wide range of additive processes generated from fractional Brownian motions, stable processes, Brownian sheets, etc. As an application, limit inf type LIL are proved for additive stable processes. 1