Pricing Basket Options by Polynomial Approximations

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

Pricing Basket Options by Polynomial Approximations

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

Characteristics of the Global Radio Frequency Interference in the Protected Portion of L-Band

The National Aeronautics and Space Administration’s (NASA’s) Soil Moisture Active–Passive (SMAP) radiometer has been providing geolocated power moments measured within a 24 MHz band in the protected portion of L-band, i.e., 1400–1424 MHz, with 1.2 ms and 1.5 MHz time and frequency resolutions, as its Level 1A data. This paper presents important spectral and temporal properties of the radio frequency interference (RFI) in the protected portion of L-band using SMAP Level 1A data. Maximum and average bandwidth and duration of RFI signals, average RFI-free spectrum availability, and variations in such properties between ascending and descending satellite orbits have been reported across the world. The average bandwidth and duration of individual RFI sources have been found to be usually less than 4.5 MHz and 4.8 ms; and the average RFI-free spectrum is larger than 20 MHz in most regions with exceptions over the Middle East and Central and Eastern Asia. It has also been shown that, the bandwidth and duration of RFI signals can vary as much as 10 MHz and 10 ms, respectively, between ascending and descending orbits over certain locations. Furthermore, to identify frequencies susceptible to RFI contamination in the protected portion of L-band, observed RFI signals have been assigned to individual 1.5 MHz SMAP channels according to their frequencies. It has been demonstrated that, contrary to common perception, the center of the protected portion can be as RFI contaminated as its edges. Finally, there have been no significant correlations noted among different RFI properties such as amplitude, bandwidth, and duration within the 1400–1424 MHz band.

Power moments of automorphic L-functions related to Maass forms for SL 3(ℤ)

Let f f be a self-dual Hecke-Maass eigenform for the group S L 3 ( Z ) S{L}_{3}\left({\mathbb{Z}}) . For 1 2 < σ < 1 \frac{1}{2}\lt \sigma \lt 1 fixed we define m ( σ ) m\left(\sigma ) ( ≥ 2 \ge 2 ) as the supremum of all numbers m m such that ∫ 1 T ∣ L ( s , f ) ∣ m d t ≪ f , ε T 1 + ε , \underset{1}{\overset{T}{\int }}| L\left(s,f){| }^{m}{\rm{d}}t{\ll }_{f,\varepsilon }{T}^{1+\varepsilon }, where L ( s , f ) L\left(s,f) is the Godement-Jacquet L-function related to f f . In this paper, we first show the lower bound of m ( σ ) m\left(\sigma ) for 2 3 < σ < 1 \frac{2}{3}\lt \sigma \lt 1 . Then we establish asymptotic formulas for the second, fourth and sixth powers of L ( s , f ) L\left(s,f) as applications.

Power Moments of the Riesz Mean Error Term of Symmetric Square L-Function in Short Intervals

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2,Z) and let L(s,sym2f)=∑n=1∞cnn−s,ℜs>1 denote the symmetric square L-function of f. In this paper, we consider the Riesz mean of the form Dρ(x;sym2f)=L(0,sym2f)Γ(ρ+1)xρ+Δρ(x;sym2f) and derive the asymptotic formulas for ∫T−HT+HΔρk(x;sym2f)dx, when k≥3.

The moment problem on curves with bumps

The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.

Function Polynomization Methods and their Applications

A class of semicontinuous quasiconvex methods of summation of Fourier – Chebyshev series is studied. Upper bounds are obtained for the norms of the corresponding operators in the space of continuous functions. The convergence of means in the metric of space is established. The summability at break points of the first kind is also considered. Processes for restoring functions from a given sequence of power moments are proposed. Ways of generalizing the results and extending them to the case of summability at Lebesgue points are indicated.