Several notions of stochastic convexity and concavity and their properties are studied in this paper. Efficient sample path approaches are developed in order to verify the occurrence of these notions ...

In the article, we prove that the function x→ ( 1−x ) p K( x ) is logarithmically concave on (0, 1) if and only if p ≥ 7/32, the function x→K( x )/log( 1+4/ 1−x ) is convex on (0, 1) and the function ...

Sean Ross is a strategic adviser at 1031x.com, Investopedia contributor, and the founder and manager of Free Lances Ltd. Cierra Murry is an expert in banking, credit cards, investing, loans, mortgages ...

Gordon Scott has been an active investor and technical analyst or 20+ years. He is a Chartered Market Technician (CMT). Negative convexity exists when the shape of a bond's yield curve is concave. A ...