We construct an exotic one-parameter semigroup of endomorphisms of a symmetric cone $C$, whose generator is not the sum of a Lie group generator and an endomorphism of $C$. The question is motivated by the theory of affine processes on symmetric cones, which plays an important role in mathematical finance. On the other hand, theoretical question that we solve in this paper seems to have been implicitly open even much longer then this motivation suggests.
COBISS.SI-ID: 17257561
In less than five years a surprisingly high level of attention has built up in the possible connection between internet search data and stock prices. It is the main aim of this paper to point out how this connection may depend heavily on different regimes of the market, i.e. the bear market vs. the bull market. We consider three types of internet search data (relative Google search frequencies of company tickers, relative Google search frequencies of company names and page visits of Wikipedia articles about individual companies) and a substantial sample of companies which are members of the S&P 500 index. We discover two inverse patterns in stock prices: in the bear market what we propose to term a "merry frown" and in bull market a "sour smile", both clearly seen especially for the Wikipedia data. We propose market neutral strategies that exploit these new patterns and yield up to 17% in average annual return during our sample period from 2008 to 2013.
COBISS.SI-ID: 17368921
We consider polynomials in noncommuting variables that admit sum of hermitian squares and commutators decompositions. We recall algorithms for finding decompositions of this type that are based on semidefinite programming. The main part of the article investigates how to find such decomposition with rational coefficients if the original polynomial has rational coefficients. We show that the numerical evidence, obtained by the Gram matrix method and semidefinite programming, which is usually an almost feasible point, can be frequently tweaked to obtain an exact certificate using rational numbers. In the presence of Slater points, the Peyrl-Parrilo rounding and projecting method applies. On the other hand, in the absence of strict feasibility, a variant of the facial reduction is proposed to reduce the size of the semidefinite program and to enforce the existence of Slater points. All these methods are implemented in our open source computer algebra package NCSOStools. Throughout the paper many worked out examples are presented to illustrate our results.
COBISS.SI-ID: 17280089