Currency Risk Hedging With Time-Varying Correlations

This paper studies currency risk hedge when volatilities and correlations of forward currency contracts and underlying assets returns are all time-varying.  A multivariate GARCH model with time-varying correlations is adopted to fit the dynamic structure of the conditional volatilities and correlations. The conditional risk-minimizing hedge strategies are estimated for an international portfolio of the US, UK and Switzerland stocks, for the period of February of 1973 to March of 2002. The empirical results show that the optimal dynamic hedging strategies can capture partially the currency fluctuations, and greatly reduce the currency risk and enhance the risk-adjusted returns of the portfolio with significant foreign currency exposures

Catalytic Asymmetric Bond Constructions in Complex Molecule Synthesis. An Approach to the Synthesis of Spirolide C and the Development of Enantioselective Enolate Hydroxylation Reactions

The asymmetric synthesis of spirolide C, a highly potent marine toxin, has been investigated in our laboratory. The construction of C7-C28 bis-spiroketal was completed through a strategy utilizing an intermolecular Stetter reaction and a biomimetic ketalization process. Stereocenters were set in great diastereo- and enantioselectivity via asymmetric catalysis. The efficiency of the synthesis was demonstrated by its convergency and high yields. A cinchona alkaloid catalyzed ketene-oxaziridine cyclocondensation has been developed to provide an access to enantioenriched α-hydroxy carbonyl compounds. The oxazolidinones arising from the cyclocondensation were converted to various α-hydroxy carbonyl compounds via nucleophilic ring openings. Greater than 98% ee was achieved in oxazolidinone formation and the subsequent ring openings proceeded with retention of the ee or minor epimerization

The anisotropic Kerr nonlinear refractive index of the beta-barium borate (\beta-BaB2O4) nonlinear crystal

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (\beta-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant $\chi^{(3)}$ cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We find that the Kerr nonlinear tensor component responsible for self-phase modulation in cascading is considerably larger than what has been used to date. We evaluate the impact of using such a cubic anisotropic response in ultrafast cascading experiments.Comment: Updated version, comments on experiments from the literature welcom

Efficient Regression in Time Series Partial Linear Models

This paper studies efficient estimation of partial linear regression in time series models. In particular, it combines two topics that have attracted a good deal of attention in econometrics, viz. spectral regression and partial linear regression, and proposes an efficient frequency domain estimator for partial linear models with serially correlated residuals. A nonparametric treatment of regression errors is permitted so that it is not necessary to be explicit about the dynamic specification of the errors other than to assume stationarity. A new concept of weak dependence is introduced based on regularity conditions on the joint density. Under these and some other regularity conditions, it is shown that the spectral estimator is root-n-consistent, asymptotically normal, and asymptotically efficient.Efficient estimation, Partial linear regression, Spectral regression, Kernel estimation, Nonparametric, Semiparametric, Weak dependence

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

Experimental data of femtosecond thick-crystal second-harmonic generation shows that when tuning away from phase matching, a dominating narrow spectral peak appears in the second harmonic that can be tuned over 100's of nm by changing the phase-mismatch parameter. Traditional theory explains this as phase matching between a sideband in the broadband pump to its second-harmonic. However, our experiment is conducted under high input intensities and instead shows excellent quantitative agreement with a nonlocal theory describing cascaded quadratic nonlinearities. This theory explains the detuned peak as a nonlocal resonance that arises due to phase-matching between the pump and a detuned second-harmonic frequency, but where in contrast to the traditional theory the pump is assumed dispersion-free. As a soliton is inherently dispersion-free, the agreement between our experiment and the nonlocal theory indirectly proves that we have observed a soliton-induced nonlocal resonance. The soliton exists in the self-defocusing regime of the cascaded nonlinear interaction and in the normal dispersion regime of the crystal, and needs high input intensities to become excited.Comment: submitted, revised versio

Efficient Regression in Time Series Partial Linear Models

This paper studies efficient estimation of partial linear regression in time series models. In particular, it combines two topics that have attracted a good deal of attention in econometrics, viz. spectral regression and partial linear regression, and proposes an efficient frequency domain estimator for partial linear models with serially correlated residuals. A nonparametric treatment of regression errors is permitted so that it is not necessary to be explicit about the dynamic specification of the errors other than to assume stationarity. A new concept of weak dependence is introduced based on regularity conditions on the joint density. Under these and some other regularity conditions, it is shown that the spectral estimator is root-n-consistent, asymptotically normal, and asymptotically efficient

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

We interpret the purely spectral forward Maxwell equation with up to 3${^{\rm rd}}$ order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named nonlinear wave equation in frequency domain, includes both quadratic and cubic nonlinearities, delayed Raman effects and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due to competition between self-steepening, Raman effects and self-steepening-like effects from cascading originating in the group-velocity mismatch between the pump and second harmonic. We analyze the first-order contributions, and show that this balance can be broken to create fast or slow pulses. Through further simulations we demonstrate few-cycle compressed solitons in extremely short crystals, where spectral phenomena such as blue/red shifting, non-stationary radiation in accordance with the non-local phase matching condition and dispersive-wave generation are observed and marked, which help improving the experimental knowledge of cascading nonlinear soliton pulse compression