Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes

Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price without nested simulation, under the jump-diffusion setting. By exploiting the martingale representation theorem for jump processes on the dual martingale, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal-dual algorithm, therefore significantly improves the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our proposed algorithm

Generalization Bounds for Representative Domain Adaptation

In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or briefly called representative domain adaptation). In particular, we use the integral probability metric to measure the difference between the distributions of two domains and meanwhile compare it with the H-divergence and the discrepancy distance. We develop the Hoeffding-type, the Bennett-type and the McDiarmid-type deviation inequalities for multiple domains respectively, and then present the symmetrization inequality for representative domain adaptation. Next, we use the derived inequalities to obtain the Hoeffding-type and the Bennett-type generalization bounds respectively, both of which are based on the uniform entropy number. Moreover, we present the generalization bounds based on the Rademacher complexity. Finally, we analyze the asymptotic convergence and the rate of convergence of the learning process for representative domain adaptation. We discuss the factors that affect the asymptotic behavior of the learning process and the numerical experiments support our theoretical findings as well. Meanwhile, we give a comparison with the existing results of domain adaptation and the classical results under the same-distribution assumption.Comment: arXiv admin note: substantial text overlap with arXiv:1304.157

Adhesion Enhancement of Diamond Coating on WC-Co Substrates Through Interlayer Design

Diamond coating with sufficient adhesion on WC-Co cutting tools is expected to significantly increase their cutting performance. However, the adhesion is always limited by the formation of graphitic soot in the interface due to the catalytic effect of Co on graphite formation. Moreover, the low nucleation density and the high thermal stress in the coatings also result in poor adhesion. The introduction of interlayer is one of the available approaches to enhance the coating-substrate interfacial adhesion. The goal of this project is to improve the adhesion through the optimization of interlayer design. The Al2O3 and Ta mono-interlayer, Al-Al2O3, Al-AlN, Al2O3-Ta and Al-Ta duplex interlayer systems have been developed in this study. These interlayer materials were prepared using a magnetron sputtering method, and diamond coating were deposited on them using microwave plasma enhanced chemical vapor deposition. In addition, different diamond seeding conditions have been studied to increase the diamond nucleation density. Grazing incident X-ray diffraction was carried out to determine the phase components in the Al-Al2O3 and Al-AlN interlayers. Raman spectroscopy and scanning electron microscopy were used to evaluate the quality, morphology and microstructure of the deposited diamond coatings. Rockwell C indentation testing was performed to evaluate the adhesion of the coatings. To elucidate the coating failure mechanism, the compositions around the delaminated spots of diamond coatings after indentation were identified by Energy-dispersive X-ray spectroscopy. To evaluate the tribological properties of the diamond coatings, the diamond coated WC-Co sheets were rubbed against steel and alumina balls respectively. The results show that continuous diamond coatings were achieved on Al2O3, Al-Al2O3, Al-AlN and Al-Ta interlayered substrates, whereas a graphite layer was still formed with the Ta monolayer or Al2O3-Ta duplex layer accompanied by an easy spallation of diamond coatings. The Al interlayer has played an important role in obtaining high purity diamond by in-situ forming an alumina barrier layer. Especially, the diamond coating deposited with an Al-AlN interlayer exhibits superior interfacial adhesion in comparison with all the other interlayers. Meanwhile, seeding with nano-diamond particles is more efficient than micro-diamond particles for improving the diamond nucleation density on Al-AlN interlayered substrates. Furthermore, the diamond coated WC-Co sheets possess lower coefficient of friction and wear rate than bare sheets when rubbing against either steel or alumina balls

Constrained knots in lens spaces

In this paper, we study a special family of $(1,1)$ knots called constrained knots, which includes 2-bridge knots in the 3-sphere $S^3$ and simple knots in lens spaces. Constrained knots are parameterized by five integers and characterized by the distribution of spin$^c$ structures in the corresponding $(1,1)$ diagrams. The knot Floer homology $\widehat{HFK}$ of a constrained knot is thin. We obtain a complete classification of constrained knots based on the calculation of $\widehat{HFK}$ and presentations of knot groups. We provide many examples of constrained knots constructed from surgeries on links in $S^3$, which are related to 2-bridge knots and 1-bridge braids. We also show many examples of constrained knots whose knot complements are orientable hyperbolic 1-cusped manifolds with simple ideal triangulations.Comment: v2, 50 pages, 21 figures. There are no essential changes about arguments and proofs. Many details and comments are added. A table about constrained knots is added in the introduction. Data and codes can be found at https://doi.org/10.7910/DVN/GLFLH

Risk-Taking and CEO Compensation: CEO Pay Slice Versus Pay-Volatility Sensitivity

This paper aims to analyze the impacts of compensation incentives and CEO power on firm’s risk-taking by using stock return volatility (Srisk) and earnings volatility (Erisk) as the proxies of firm’s risk-taking level, and by using pay-volatility sensitivity (PVS) and CEO-pay slice (CPS) as the proxies of compensation incentives and CEO power, respectively. By applying ordinary least square (OLS) regression and two-stage least square (2SLS) regression on obtained data, this paper provides strong empirical evidence that PVS and CPS have negative impact on earnings volatility and stock return volatility. In addition, the negative impact of PVS on managerial risk-taking is greater for CEOs with lower CPS than that for CEOs with higher CPS. That is, EBC discourages CEOs from taking more risks, and more powerful CEOs are less risk-averse than less powerful CEOs when granted EBC