Optimal Choice Models for Executing Time to American Options

Based on the structure models of options pricing on non-dividend-paying stock [16], this paper presents the choosing models and methods of optimal time of executing an American options for the first time. By using the models and methods, we can find the choosing criterion and optimal time to exercise the American options, i.e. the product of options price and its occurring probability is at maximum. So we can decide that an American option should be exercised or not in any time. The conclusions in this paper are more important in its consulting effect for single trader and organization investors to make their security market trade.partial distribution; American options; structure pricing; optimal executing; analytic formula

Structural response of concrete-filled elliptical steel hollow sections under eccentric compression

The purpose of this research is to examine the behaviour of elliptical concrete-filled steel tubular stub columns under a combination of axial force and bending moment. Most of the research carried out to date involving concrete-filled steel sections has focussed on circular and rectangular tubes, with each shape exhibiting distinct behaviour. The degree of concrete confinement provided by the hollow section wall has been studied under pure compression but remains ambiguous for combined compressive and bending loads, with no current design provision for this loading combination. To explore the structural behaviour, laboratory tests were carried out using eight stub columns of two different tube wall thicknesses and applying axial compression under various eccentricities. Moment-rotation relationships were produced for each specimen to establish the influence of cross-section dimension and axis of bending on overall response. Full 3D finite element models were developed, comparing the effect of different material constitutive models, until good agreement was found. Finally, analytical interaction curves were generated assuming plastic behaviour and compared with the experimental and finite element results. Ground work provided from these tests paves the way for the development of future design guidelines on the member level

Constructing Fewer Open Cells by GCD Computation in CAD Projection

A new projection operator based on cylindrical algebraic decomposition (CAD) is proposed. The new operator computes the intersection of projection factor sets produced by different CAD projection orders. In other words, it computes the gcd of projection polynomials in the same variables produced by different CAD projection orders. We prove that the new operator still guarantees obtaining at least one sample point from every connected component of the highest dimension, and therefore, can be used for testing semi-definiteness of polynomials. Although the complexity of the new method is still doubly exponential, in many cases, the new operator does produce smaller projection factor sets and fewer open cells. Some examples of testing semi-definiteness of polynomials, which are difficult to be solved by existing tools, have been worked out efficiently by our program based on the new method.Comment: Accepted by ISSAC 2014 (July 23--25, 2014, Kobe, Japan