In this paper we study window barrier options, where a single constant continuously-monitored barrier prevails for a period that commences strictly after the start date of the option and terminates strictly before expiry. We determine valuation formulae within a limited deterministic...

Let X, W be independent real-valued random variables with finite expectation and E(W) = 0. We prove that only in the case W=0 the conditional expectation E(XX+W) coincides with X+W. The result is a consequence of the following cancellation theorem: Let P, Q, R be Borel probability measures on...

In this paper, we illustrate how the Fourier transform can be used to compute the posterior mean and variance of a location parameter when its prior belongs to a location-scale family of densities. Furthermore, if the likelihood function satisfies some conditions, an estimator of the frequentist...