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In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces ¯, (,) in quantum cohomology. [ 1 ] : §1 [ 2 ] [ 3 ] These moduli spaces are smooth orbifolds whenever the target space is convex.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
The concept of strong convexity extends and parametrizes the notion of strict convexity. Intuitively, a strongly-convex function is a function that grows as fast as a quadratic function. [11] A strongly convex function is also strictly convex, but not vice versa.
The specifics vary from bond to bond, but callable bonds always have one thing in common — the issuer can pay off the bond early. As an investor, there are potential benefits and drawbacks to ...
By issuing numerous callable bonds, they have a natural hedge, as they can then call their own issues and refinance at a lower rate. The price behaviour of a callable bond is the opposite of that of puttable bond. Since call option and put option are not mutually exclusive, a bond may have both options embedded. [3]
Convexity is not strictly necessary for Brouwer's fixed-point theorem. Because the properties involved (continuity, being a fixed point) are invariant under homeomorphisms , Brouwer's fixed-point theorem is equivalent to forms in which the domain is required to be a closed unit ball D n {\displaystyle D^{n}} .
The elements of 𝒞 are called convex sets and the pair (X, 𝒞) is called a convexity space. For the ordinary convexity, the first two axioms hold, and the third one is trivial. For an alternative definition of abstract convexity, more suited to discrete geometry, see the convex geometries associated with antimatroids.
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