A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.

The impact of chemotherapy dose density and dose intensity on breast cancer outcome: what have we learned?

Optimising chemotherapy dose density and dose intensity are strategies aimed at improving outcomes in adjuvant therapy for patients with breast cancer. There are, in theory, at least five models allowing the delivery of a higher overall drug dose intensity. These are reviewed in this article and vary according to three main variables: the dose per course, the interval between doses and the total cumulative dose. Cyclophosphamide, anthracyclines and taxanes are among the most active agents for the treatment of breast cancer and, as such, they have been or are currently the focus of prospective, randomised clinical trials testing some of these dose-intensity models in the adjuvant setting. The results of recent trials suggest that anthracyclines, but not cyclophosphamide, are associated with better outcomes if used at higher doses per course and at higher cumulative doses. However, care has to be taken with premenopausal women where an increased dose of anthracycline per course but a reduced cumulative dose appears to produce a worse outcome. Moreover, decreasing the interval between doses, for anthracyclines and cyclophosphamide, does not seem to provide, so far, additional benefits for women with locally advanced breast cancer. This approach is not feasible with docetaxel, since an increase in dose density induces unwanted side-effects. These results represent our current state of knowledge, but clinical trials are being performed to evaluate further the effect of dose intensity, dose density and cumulative dose of key therapeutic agents on patient outcomes.