Superconducting cosmic strings as sources of cosmological fast radio bursts

In this paper we calculate the radio burst signals from three kinds of structures of superconducting cosmic strings. By taking into account the observational factors including scattering and relativistic effects, we derive the event rate of radio bursts as a function of redshift with the theoretical parameters $G\mu$ and $\mathcal{I}$ of superconducting strings. Our analyses show that cusps and kinks may have noticeable contributions to the event rate and in most cases cusps would dominate the contribution, while the kink-kink collisions tend to have secondary effects. By fitting theoretical predictions with the normalized data of fast radio bursts, we for the first time constrain the parameter space of superconducting strings and report that the parameter space of $G\mu \sim [10^{-14}, 10^{-12}]$ and $\mathcal{I} \sim [10^{-1}, 10^{2}] ~ \rm{GeV}$ fit the observation well although the statistic significance is low due to the lack of observational data. Moreover, we derive two types of best fittings, with one being dominated by cusps with a redshift $z = 1.3$, and the other dominated by kinks at the range of the maximal event rate.Comment: 13 pages, 2 figures, 1 table; references update

Bounding Option Prices Using SDP With Change Of Numeraire

Recently, given the first few moments, tight upper and lower bounds of the no arbitrage prices can be obtained by solving semidefinite programming (SDP) or linear programming (LP) problems. In this paper, we compare SDP and LP formulations of the European-style options pricing problem and prefer SDP formulations due to the simplicity of moments constraints. We propose to employ the technique of change of numeraire when using SDP to bound the European type of options. In fact, this problem can then be cast as a truncated Hausdorff moment problem which has necessary and sufficient moment conditions expressed by positive semidefinite moment and localizing matrices. With four moments information we show stable numerical results for bounding European call options and exchange options. Moreover, A hedging strategy is also identified by the dual formulation.moments of measures, semidefinite programming, linear programming, options pricing, change of numeraire