Optimal stopping for Lévy processes and affine functions

32 pagesOptimal stoppingThis paper studies an optimal stopping problem for Lévy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time. We propose a method which allows to obtain the optimal threshold. Moreover this method allows to avoid long calculations of the integro-differential operatorused in the usual proofs

Arr\^et optimal pour les processus de Markov forts et les fonctions affines

In this Note we study optimal stopping problems for strong Markov processes and affine functions. We give a justification of the Snell envelope form using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time

A note on the computation of an actuarial Waring formula in the finite-exchangeable case

We present in this paper the actuarial Waring formula, which is used in several fields, like life-insurance or credit risk. In a particular framework where considered random variables are exchangeable, we show that some problems can occur when using this formula. We propose alternative recursions in order to improve the complexity of the calculations, and to cope with the numerical instability of the formula.

The Master’s Theory of Everything:A review of Iain McGilchrist’s The Matter with Things: Our Brains, Our Delusions, and the Unmaking of the World

An extended review of "The Matter with Things", by Iain McGilchrist, with some reflections on the implications of the brain lateralization hypothesis for theological anthropology and science & religio