This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.
The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original question, i.e.,...
In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.