Log-free zero density estimates for automorphic LL-functions

We prove a log-free zero density estimate for automorphic $L$-functions defined over a number field $k$. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree $n$ over $k$ (for any $n$) that an effective Chebotarev density theorem and a bound on $\ell$-torsion in class groups hold for almost all fields in the family.Comment: 43 page

Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies

In this paper, we consider the net loss of a life insurance company issuing identical equity-linked pure endowment contracts in the case of periodic premiums. Under this construction, financial risks as well as the mortality risk are included. Based on Møller (1998), we particularly investigate the situation where the company applies a time-discretized risk-minimizing hedging strategy, i.e., a trading restriction is imposed on a continuous-time risk-minimizing strategy. Therefore, the considered model is incomplete where the incompleteness results not only from the mortality risk but also from the trading restrictions. Through an illustrative example, it is observed from the simulations that a substantial reduction in the ruin probability is achieved by using the time-discretized risk-minimizing strategy. However, as the hedging frequency is set higher, this advantage almost disappears, because a higher frequency leads to more hedging errors which constitute a vital part of the hedger’s net loss. In order to improve the simulated results, another type of discrete-time risk-minimizing strategy is taken into consideration. It is obtained by discretizing the hedging model instead of the hedging strategy. For this purpose, Møller’s (2001) discrete-time (binomial) risk-minimizing strategy is adopted. For both strategies, a number of sensitivity analyses are carried out, e.g. how the ruin probability changes with the fair combination of the minimum interest rate guarantee and the participation rate.Net Loss, Discrete-time Risk-minimizing Hedging Strategies, Pure Endowment Equity-linked Life Insurance

Serial perturbation of MinK in IKs implies an alpha-helical transmembrane span traversing the channel corpus.

I(Ks) channels contain four pore-forming KCNQ1 subunits and two accessory MinK subunits. MinK influences surface expression, voltage-dependence of gating, conduction, and pharmacology to yield the attributes characteristic of native channels in heart. The structure and location of the MinK transmembrane domain (TMD) remains a matter of scrutiny. As perturbation of gating analysis has correctly inferred the peripheral location and alpha-helical nature of TMDs in pore-forming subunits, the method is applied here to human MinK. Tryptophan and Asparagine substitution at 23 consecutive sites yields perturbation with alpha-helical periodicity (residues 44-56) followed by an alternating impact pattern (residues 56-63). Arginine substitution across the span suggests that as few as eight sites are occluded from aqueous solution (residues 50-57). We favor a TMD model that is alpha-helical with the external portion of the span at a lipid-protein boundary and the inner portion within the channel corpus in complex interactions