Guaranteed Inertia Functions in Dynamical Games.

This paper deals with inertia functions in control theory introduced in Aubin, Bernardo and Saint-Pierre (2004, 2005) and their adaptation to dynamical games. The inertia function associates with any initial state-control pair the smallest of the worst norms over time of the velocities of the controls regulating viable evolutions. For tychastic systems (parameterized systems where the parameters are tyches, disturbances, perturbations, etc.), the palicinesia of a tyche measure the worst norm over time of the velocities of the tyches. The palicinesia function is the largest palicinesia threshold c such that all evolutions with palicinesia smaller than or equal to c are viable. For dynamical games where one parameter is the control and the other one is a tyche (games against nature or robust control), we define the guaranteed inertia function associated with any initial state-control-tyche triple the best of the worst of the norms of the velocities of the controls and of the tyches and study their properties. Viability Characterizations and Hamilton-Jacobi equations of which these inertia and palicinesia functions are solutions are provided.Viability; dynamical games; inertia function; Tychastic systems; palicinesia;

Planning for "The Greatest Digitization Project on Earth" with the P. T. Barnum Collections of The Barnum Museum Foundation

The Barnum Museum Foundation, Inc. requests a grant of $40,000 that will enable The Barnum Museum and Bridgeport Public Library to work with a team of consultants to create a comprehensive plan for digitization and global access to important humanities collections. The year-long project is designed to result in the ???road map??? critical to implementing a well-managed digitization project that can fully realize its objectives for preservation and access. The project will improve intellectual control of the two institutions??? related P. T. Barnum collections, and incorporate a range of activities that utilize the knowledge, experience and expertise of the team members. The project will lead to a plan for broad access to these significant humanities resources and create digital content that would be placed in an aggregate digital resource repository with a curated platform

Differential games through viability theory : old and recent results.

This article is devoted to a survey of results for differential games obtained through Viability Theory. We recall the basic theory for differential games (obtained in the 1990s), but we also give an overview of recent advances in the following areas : games with hard constraints, stochastic differential games, and hybrid differential games. We also discuss several applications.Game theory; Differential game; viability algorithm;

Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.

We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall “compute” the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the Pujal—Saint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.dynamic games; dynamic valuation; tychastic control systems; management of portfolio;

Disinforming the Public

Saint-Sernin Bertrand, Frank Marie-Thérèse, Mignaval Pierre. N° 54 — SAINT-SERNIN Bertrand. In: Témoins et acteurs des politiques de l'éducation depuis la Libération. Tome 4 - Inventaire de soixante-quatre entretiens. Paris : Institut national de recherche pédagogique, 2005. pp. 152-154. (Témoins et acteurs des politiques de l'éducation, 1

Viabilist and Tychastic Approaches to Guaranteed ALM Problem.

This study reconsiders the problem of hedging a liability by a portfolio made of a riskless asset and an underlying (underlying).Asset and Liability Management; Viability theory;