On the light quark mass effects in Higgs boson production in gluon fusion

Production of Higgs bosons at the LHC is affected by the contribution of light quarks, that mediate the gg \to Hg transition. Although their impact is suppressed by small Yukawa couplings, it is enhanced by large logarithms of the ratio of the Higgs boson mass or its transverse momentum to light quark masses. We study the origin of this enhancement, focusing on the abelian corrections to gg \to Hg amplitudes of the form (C_F alphas L^{2})^n, where $L \in { ln(s/mb^2), ln(p_\perp^2/mb^2) }. We show how these non-Sudakov double logarithmic terms can be resummed to all orders in the strong coupling constant. Interestingly, we find that the transverse momentum dependence of these corrections is very weak due to a peculiar cancellation between different logarithmic terms. Although the abelian part of QCD corrections is not expected to be dominant, it can be used to estimate missing higher-order corrections to light quark contributions to Higgs boson production at the LHC.Comment: 18 pages, 2 figure

Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets

The authors use the efficient hedging methodology for optimal pricing and hedging of equitylinked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, they consider a policy that pays the maximum of the values of n risky assets at some maturity date T , provided that the policyholder survives to T . Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. The authors show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. They also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are derived for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.Financial markets;

Independence in computable algebra

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and difference closed fields with the relevant notions of independence. To cover these classes of structures we introduce a new technique of safe extensions that was not necessary for the previously known results of this kind. We will then apply our techniques to derive new corollaries on the number of computable presentations of these structures. The condition also implies classical and new results on vector spaces, algebraically closed fields, torsion-free abelian groups and Archimedean ordered abelian groups.Comment: 24 page