Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

In a financial market with one riskless asset and n risky assets whose prices are lognormal, we solve in a closed form the problem of a pension fund maximizing the expected CRRA utility of its surplus till the (stochastic) death time of a representative agent. We consider a unique asset allocation problem for both accumulation and decumulation phases. The optimal investment in the risky assets must decrease during the first phase and increase during the second one. We accordingly suggest it is not optimal to manage the two phases separately, and outsourcing of allocation decisions should be avoided in both phases. JEL: G23, G11 MSC 2000: 62P05, 91B28, 91B30, 91B70, 93E20     

A counter-example to the characterization of the discontinuous value function of control problems with reflectionUn contre-exemple à la caractérisation de la fonction-valeur discontinue d'un problème de contrôle réfléchi

We consider a finite horizon deterministic optimal control problem with reflection. The final cost is assumed to be merely a locally bounded function which leads to a discontinuous value function. We address the question of the characterization of the value function as the unique solution of an Hamilton–Jacobi equation with Neumann boundary conditions. We follow the discontinuous approach developed by Barles and Perthame for problems set in the whole space. We prove that the minimal and maximal discontinuous viscosity solutions of the associated Hamilton–Jacobi can be written in terms of value functions of control problems with reflection. Nethertheless, we construct a counter-example showing that the value function is not the unique solution of the equation. To cite this article: O. Ley, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 469–473.     

Observations of cavitation erosion pit formation

Previous investigations showed that a single cavitation bubble collapse can cause more than one erosion pit (Philipp & Lauterborn [1]). But our preliminary study showed just the opposite – that in some cases a single cavitation pit can result from more than one cavitation event. The present study shows deeper investigation of this phenomenon. An investigation of the erosion effects of ultrasonic cavitation on a thin aluminum foil was made. In the study we observed the formation of individual pits by means of high speed cameras (>1000 fps) and quantitatively evaluated the series of images by stereoscopy and the shape from shading method. This enabled the reconstruction of the time evolution of the pit shape. Results show how the foil is deformed several times before a hole is finally punctured. It was determined that larger single pits result from several impacts of shock waves on the same area, which means that they are merely special cases of pit clusters (pit clusters where pits overlap perfectly). Finally it was shown that a thin foil, which is subjected to cavitation, behaves as a membrane. It was concluded that the physics behind erosion depends significantly on the means of generating cavitation (acoustic, hydrodynamic, laser light) and the specimen characteristics (thin foil, massive specimen), which makes comparison of results of materials resistance to cavitation from different experimental set-ups questionable.Further development of the shape from shading method in the scope of cavitation erosion testing will enable better evaluation of cavitation erosion models.     

Use of a microelectromechanical mirror for adaptive optics in the human eye

Ophthalmic instrumentation equipped with adaptive optics offers the possibility of rapid and automated correction of the eye's optics for improving vision and for improving images of the retina. One factor that limits the widespread implementation of adaptive optics is the cost of the wave-front corrector, such as a deformable mirror. In addition, the large apertures of these elements require high pupil magnification, and hence the systems tend to be physically large. We present what are believed to be the first closed-loop results when a compact, low-cost, surface micromachined, microelectromechanical mirror is used in a vision adaptive-optics system. The correction performance of the mirror is shown to be comparable to that of a Xinetics mirror for a 4.6-mm pupil size. Furthermore, for a pupil diameter of 6.0-mm, the residual rms error is reduced from 0.36 to 0.12 microm and individual photoreceptors are resolved at a pupil eccentricity of 1 degrees from the fovea.     

Validation and generalization of DEA and its uses

Summary Rapidly expanding uses of DEA have been accompanied by developments which have enhanced its power and enlarged its utility for additional applications. Developments covered in the present paper include simulation studies comparing DEA with competing forms of statistical regressions. Other studies covered show how these two approaches can be combined in complementary fashion. Another part of this paper deals with Chance Constrained Programming formulations which incorporate probabilistic elements into DEA. Included also are discussions of statistical characterizations with accompanying tests of statistical significance for DEA efficiency evaluations. This paper concludes with uses of DEA in “discovery processes”-processes that need strengthening (and encouragemnt) in contemporary social science and management science research. Suggestions are made for additional research on further developments which extend to uses of DEA to provide new approaches in economics (including econometrics), management and psychology and an Appendix introduces new or recently developed efficiency measures for use in DEA. Invited by J. T. Pastor     

Pierre Turq,an inspirational scientist in charge and at interfaces

Pierre Turq has made decisive contributions to the theory and to the multiscale simulation of charged systems, such as molten salts, electrolyte solutions and colloidal suspensions, in the bulk, at interfaces and under confinement. His research line focussed on dynamical properties and was characterised by constant efforts to connect his theoretical work to both experiments and practical applications. In this article, his colleagues and former students pay a tribute to his past and current research interests by illustrating some recent developments accomplished in his laboratory.     

Dual-mode registration of dynamic contrast-enhanced ultrasound combining tissue and contrast sequences

This study proposes a new method for automatic, iterative image registration in the context of dynamic contrast-enhanced ultrasound (DCE-US) imaging. By constructing a cost function of image registration using a combination of the tissue and contrast-microbubble responses, this new method, referred to as dual-mode registration, performs alignment based on both tissue and vascular structures. Data from five focal liver lesions (FLLs) were used for the evaluation. Automatic registration based on the dual-mode registration technique and tissue-mode registration obtained using the linear response image sequence alone were compared to manual alignment of the sequence by an expert. Comparison of the maximum distance between the transformations applied by the automatic registration techniques and those from expert manual registration reference showed that the dual-mode registration provided better precision than the tissue-mode registration for all cases. The reduction of maximum distance ranged from 0.25 to 9.3 mm. Dual-mode registration is also significantly better than tissue-mode registration for the five sequences with p  -values lower than 0.03$0.03$. The improved sequence alignment is also demonstrated visually by comparison of images from the sequences and the video playbacks of the motion-corrected sequences. This new registration technique better maintains a selected region of interest (ROI) within a fixed position of the image plane throughout the DCE-US sequence. This should reduce motion-related variability of the echo-power estimations and, thus, contribute to more robust perfusion quantification with DCE-US.     

DNS and LES of spark ignition with an automotive coil

The cycle to cycle combustion variability which is observed in spark-ignition engines is often caused by fluctuations of the early flame development. LES can be exploited for a better understanding and mastering of their origins. For that purpose appropriate models taking into account energy deposition, mixture ignition and transition to propagation are necessary requirements. This paper presents first DNS and LES of spark ignition with a real automotive coil and simplified pin-pin electrodes. The electrical circuit characteristics are provided by ISSIM while the energy deposition is modelled by Lagrangian particles. The ignition model is first evaluated in terms of initial spark radius on a pin-pin ignition experiment in pure air performed at CORIA and EM2C laboratories, showing that it pilots the radius of the torus formed by the initial shock wave. DNS of a quiescent lean propane/air mixture are then performed with this ignition system and a two-step mechanism. The impact of the modelled transferred energy during glow phase as well as the initial arc radius on the minimum ignition energy (MIE) are examined and compared to experimental values. Replacing the two-step chemistry by an analytically reduced mechanism leads to similar MIE but shows a different ignition kernel shape. Finally, LES of turbulent ignition using a Lagrangian arc model show a realistic prediction of the arc shape and its important role on the energy transfer location and thus on the flame kernel shape.