A BSDE approach to stochastic differential games with incomplete information

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over some martingale measures with a payoff given by the solution of a backward stochastic differential equation

Zero-sum stopping games with asymmetric information

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples

On Dynkin games with incomplete information

In this paper we investigate a game of optimal stopping with incomplete information. There are two players of which only one is informed about the precise structure of the game. Observing the informed player the uninformed player is given the possibility to guess the missing information. We show that these games have a value which can be characterized as a viscosity solution to a fully non-linear variational PDE. Furthermore we derive a dual representation of the value function in terms of a minimization procedure. This representation allows under some additional assumptions to determine optimal strategies for the informed player

Zero-sum stopping games with asymmetric information

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples

Jeux différentiels stochastiques à information incomplète

L'objectif de cette thèse est l'étude des jeux différentiels stochastiques à information incomplète. Nous considérons un jeu à deux joueurs adverses qui contrôlent une diffusion afin de minimiser, respectivement de maximiser un paiement spécifique. Pour modéliser l'incomplétude des informations, nous suivrons la célèbre approche d'Aumann et Maschler. Nous supposons qu'il existe des états de la nature différents dans laquelle le jeu peut avoir lieu. Avant que le jeu commence, l'état est choisi au hasard. L'information est ensuite transmise à un joueur alors que le second ne connaît que les probabilités respectives pour chaque état.Dans cette thèse nous établissons une représentationduale pour les jeux différentiels stochastiques à information incomplète. Ici, nous utilisons largement la théorie des équations différentielles stochastiques rétrogrades (EDSRs), qui se révèle être un outilindispensable dans cette étude. En outre, nous montrons comment, sous certaines restrictions, cette représentation permetde construire des stratégies optimales pour le joueur informé. Ensuite, nous donnons, en utilisant la représentation duale, une preuve particulièrement simple de la semiconvexité de la fonction valeur des jeux différentiels à information incomplète.Un autre partie de la thèse est consacré à des schémas numériques pour les jeux différentiels stochastiques à informationincomplète. Dans la dernière partie nous étudions des jeux d'arrêt optimal en temps continue, appelés jeux de Dynkin, à information incomplète. Nous établissons également une représentation duale, qui est utilisé pour déterminer des stratégies optimales pour le joueur informé dans ce cas.The objective of this thesis is the study of stochastic differential games with incomplete information. We consider a game with two opponent players who control a diffusion in order to minimize, respectively maximize a certain payoff. To model the information incompleteness we will follow the famous ansatz of Aumann and Maschler. We assume that there are different states of nature in which the game can take place. Before the game starts the state is chosen randomly. The information is then transmitted to one player while the second one only knows the respective probabilities for each state. In this thesis we establish a dual representation for stochastic differential games with incomplete information. Therein we make a vast use of the theory of backward stochastic differential equations (BSDEs), which turns out to be an indispensable tool in this study. Moreover we show how under some restrictions that this representation allows to construct optimal strategies for the informed player.Morover we give - using the dual representation - a strikingly simple proof for semiconvexity of the value function of differential games with incomplete information. Another part of this thesis is devoted to numerical schemes for stochastic differential games with incomplete information. In the last part we investigate continuous time optimal stopping games, so called Dynkin games, with information incompleteness. We show that these games have a value and a unique characterization by a fully non-linear variational PDE for which we provide a comparison principle. Also we establish a dual representation for Dynkin games with incomplete information.BREST-SCD-Bib. electronique (290199901) / SudocSudocFranceF

The chronostratigraphy of the Haua Fteah cave (Cyrenaica, northeast Libya)

The 1950s excavations by Charles McBurney in the Haua Fteah, a large karstic cave on the coast of northeast Libya, revealed a deep sequence of human occupation. Most subsequent research on North African prehistory refers to his discoveries and interpretations, but the chronology of its archaeological and geological sequences has been based on very early age determinations. This paper reports on the initial results of a comprehensive multi-method dating program undertaken as part of new work at the site, involving radiocarbon dating of charcoal, land snails and marine shell, cryptotephra investigations, optically stimulated luminescence (OSL) dating of sediments, and electron spin resonance (ESR) dating of tooth enamel. The dating samples were collected from the newly exposed and cleaned faces of the upper 7.5 m of the w14.0 m-deep McBurney trench, which contain six of the seven major cultural phases that he identified. Despite problems of sediment transport and reworking, using a Bayesian statistical model the new dating program establishes a robust framework for the five major lithostratigraphic units identified in the stratigraphic succession, and for the major cultural units. The age of two anatomically modern human mandibles found by McBurney in Layer XXXIII near the base of his Levalloiso-Mousterian phase can now be estimated to between 73 and 65 ka (thousands of years ago) at the 95.4% confidence level, within Marine Isotope Stage (MIS) 4. McBurney’s Layer XXV, associated with Upper Palaeolithic Dabban blade industries, has a clear stratigraphic relationship with Campanian Ignimbrite tephra. Microlithic Oranian technologies developed following the climax of the Last Glacial Maximum and the more microlithic Capsian in the Younger Dryas. Neolithic pottery and perhaps domestic livestock were used in the cave from the mid Holocene but there is no certain evidence for plant cultivation until the Graeco-Roman period

“Dogged” Search of Fresh Nakhla Surfaces Reveals New Alteration Textures

Special Issue: 74th Annual Meeting of the Meteoritical Society, August 8-12, 2011, London, U.K.International audienceCarbonaceous chondrites are considered as amongst the most primitive Solar System samples available. One of their primitive characteristics is their enrichment in volatile elements.This includes hydrogen, which is present in hydrated and hydroxylated minerals. More precisely, the mineralogy is expected to be dominated by phyllosilicates in the case of CM chondrites, and by Montmorillonite type clays in the case of CI. Here, in order to characterize and quantify the abundance of lowtemperature minerals in carbonaceous chondrites, we performed thermogravimetric analysis of matrix fragments of Tagish Lake, Murchison and Orgueil

Human Papilloma Virus (HPV) Oral Prevalence in Scotland (HOPSCOTCH):a feasibility study in dental settings

The purpose of this study was to test the feasibility of undertaking a full population investigation into the prevalence, incidence, and persistence of oral Human Papilloma Virus (HPV) in Scotland via dental settings. Male and female patients aged 16-69 years were recruited by Research Nurses in 3 primary care and dental outreach teaching centres and 2 General Dental Practices (GDPs), and by Dental Care Teams in 2 further GDPs. Participants completed a questionnaire (via an online tablet computer or paper) with socioeconomic, lifestyle, and sexual history items; and were followed up at 6-months for further questionnaire through appointment or post/online. Saline oral gargle/rinse samples, collected at baseline and follow-up, were subject to molecular HPV genotyping centrally. 1213 dental patients were approached and 402 individuals consented (participation rate 33.1%). 390 completed the baseline questionnaire and 380 provided a baseline oral specimen. Follow-up rate was 61.6% at 6 months. While recruitment was no different in Research Nurse vs Dental Care Team models the Nurse model ensured more rapid recruitment. There were relatively few missing responses in the questionnaire and high levels of disclosure of risk behaviours (99% answered some of the sexual history questions). Data linkage of participant data to routine health records including HPV vaccination data was successful with 99.1% matching. Oral rinse/gargle sample collection and subsequent HPV testing was feasible. Preliminary analyses found over 95% of samples to be valid for molecular HPV detection prevalence of oral HPV infection of 5.5% (95%CI 3.7, 8.3). It is feasible to recruit and follow-up dental patients largely representative / reflective of the wider population, suggesting it would be possible to undertake a study to investigate the prevalence, incidence, and determinants of oral HPV infection in dental settings