Option Valuation in Multivariate SABR Models

We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.SABR; CMS spread; displaced diffusion; Markovian projection; GyÄongy Lemma

On the Significance of the Biography and Thought of Pilgram Marpeck for a Responsible Engineering Perspective

In the general scope of an aspirational approach to engineering practice and ethics, this article follows the paradigm of learning from biography and presents Pilgram Marpeck, an engineer and Anabaptist reformer of the 16th century, as a possible early role model for the engineering professional. A biographical review of his life and all-encompassing participation in the society of his time is followed by a self-contained summary of his thought on selected topics. When considering the bearing of these on engineering ethics and practice, Marpeck\u27s thought and several of his concerns are found of current relevance

New insights for applications of Kreisselmeier's structure in robust and fault tolerant control

This paper addresses a two degree of freedom structure discussed by Kreisselmeier for the SISO case in 1999. The discussion herein considers a MIMO setting, and aims at the use of this control topology for robust and fault tolerant control. It is also shown how design barriers can be obtained for robust I/O transfer behavior assignment and robustness evaluation schemes can be devised which allow for the quantitative valuation of I/O transfer behavior degradation in the presence of plant model uncertainty. The concepts and techniques are illustrated and assessed using an in-flight simulation problem

Improved spatial separation of neutral molecules

We have developed and experimentally demonstrated an improved electrostatic deflector for the spatial separation of molecules according to their dipole-moment-to-mass ratio. The device features a very open structure that allows for significantly stronger electric fields as well as for stronger deflection without molecules crashing into the device itself. We have demonstrated its performance using the prototypical OCS molecule and we discuss opportunities regarding improved quantum-state-selectivity for complex molecules and the deflection of unpolar molecules.Comment: 6 figure

Strongly aligned and oriented molecular samples at a kHz repetition rate

We demonstrate strong adiabatic laser alignment and mixed-field orientation at kHz repetition rates. We observe degrees of alignment as large as cos\Theta=0.94 at 1 kHz operation for iodobenzene. The experimental setup consist of a kHz laser system simultaneously producing pulses of 30 fs (1.3 mJ) and 450 ps (9 mJ). A cold 1 K state-selected molecular beam is produced at the same rate by appropriate operation of an Even-Lavie valve. Quantum state selection has been obtained using an electrostatic deflector. A camera and data acquisition system records and analyzes the images on a single-shot basis. The system is capable of producing, controlling (translation and rotation) and analyzing cold molecular beams at kHz repetition rates and is, therefore, ideally suited for the recording of ultrafast dynamics in so-called "molecular movies".Comment: 6 pages, 4 figures, in press in Mol. Phys., accepted in February 2013, in final production (galley proofs done) since March 8, 2013, v3 only adds publication dat

Two-state wave packet for strong field-free molecular orientation

We demonstrate strong laser-field-free orientation of absolute-ground-state carbonyl sulfide molecules. The molecules are oriented by the combination of a 485-ps-long non-resonant laser pulse and a weak static electric field. The edges of the laser pulse create a coherent superposition of two rotational states resulting in revivals of strong transient molecular orientation after the laser pulse. The experimentally attained degree of orientation of 0.6 corresponds to the theoretical maximum for mixing of the two states. Switching off the dc field would provide the same orientation completely field-free

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This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of H∞ loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block H∞ synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV) system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter