We use bivariate C 1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and suucient condition on Bernstein-B ezier polynomials, we set the convexity preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on t...

In this paper, we obtain extensions of majorization type results and extensions of weighted Favard’s and Berwald’s inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponentially convexity and log-convexity of th...

Duration and convexity are important measures in fixed-income portfolio management. We have derived closed-form expressions for duration and convexity of zero-coupon convertibles, incorporating the impact of default risk, conversion option, and subordination. The overall effect is to shorten duration, while the effect on convexity is ambiguous. Both measures were found to be very different from...