We study a stochastic game of hiring and firing in which the employee has a random capacity which is not directly observable for the employer, and only par- tially observable for the employee. In this setting, we derive a Nash Equilibrium of strategies.

The paper studies structural credit risk models with incomplete information of the asset value. It is shown that the pricing of typical corporate securities such as equity, corporate bonds or CDSs leads to a nonlinear filtering problem. This problem cannot be tackled with standard techniques as the default time does not have an intensity under full information. We therefore transform the problem to a standard filtering problem for a stopped diffusion process. This problem is analyzed via SPDE results from the filtering literature. In particular we are able to characterize the default intensity under incomplete information in terms of the conditional density of the asset value process. Moreover, we give an explicit description of the dynamics of corporate security prices. Finally, we explain how the model can be applied to the pricing of bond and equity options and we present results from a number of numerical experiments.

Bilateral incomplete-information negotiations of multiple issues present a difficult yet common negotiation problem that is complicated to solve from a mechanism design perspective. Unlike multilateral situations, where the individual aspirations of multiple agents can potentially be used against one another to achieve socially desirable outcomes, bilateral negotiations only involve two agents; this makes the negotiations appear to be a zero-sum game pitting agent against agent. While this is essentially true, the gain of one agent is the loss of the other, with multiple issues, it is not unusual that issues are valued asymmetrically such that agents can gain on issues important to them but suffer losses on issues of less importance. Being able to make trade-offs amongst the issues to take advantage of this asymmetry allows both agents to experience overall benefit. The major complication is negotiating under the uncertainty of incomplete information, where agents do not know each other's preferences and neither agent wants to be taken advantage of by revealing its private information to the other agent, or by being too generous in its negotiating. This leaves agents stumbling in the dark trying to find appropriate trade-offs amongst issues. In this work, we introduce the Bilateral Automated Mediation (BAM) framework. The BAM framework is aimed at helping agents alleviate the difficulties of negotiating under uncertainty by formulating a negotiation environment that is suitable for creating agreements that benefit both agents jointly. Our mediator is a composition of many different negotiation ideas and methods put together in a novel third-party framework that guides agents through the agreement space of the negotiation, but instead of arbitrating a final agreement, it allows the agents themselves to ratify the final agreement.

Bilateral incomplete-information negotiations of multiple issues present a difficult yet common negotiation problem that is complicated to solve from a mechanism design perspective. Unlike multilateral situations, where the individual aspirations of multiple agents can potentially be used against one another to achieve socially desirable outcomes, bilateral negotiations only involve two agents; this makes the negotiations appear to be a zero-sum game pitting agent against agent. While this is essentially true, the gain of one agent is the loss of the other, with multiple issues, it is not unusual that issues are valued asymmetrically such that agents can gain on issues important to them but suffer losses on issues of less importance. Being able to make trade-offs amongst the issues to take advantage of this asymmetry allows both agents to experience overall benefit. The major complication is negotiating under the uncertainty of incomplete information, where agents do not know each other's preferences and neither agent wants to be taken advantage of by revealing its private information to the other agent, or by being too generous in its negotiating. This leaves agents stumbling in the dark trying to find appropriate trade-offs amongst issues. In this work, we introduce the Bilateral Automated Mediation (BAM) framework. The BAM framework is aimed at helping agents alleviate the difficulties of negotiating under uncertainty by formulating a negotiation environment that is suitable for creating agreements that benefit both agents jointly. Our mediator is a composition of many different negotiation ideas and methods put together in a novel third-party framework that guides agents through the agreement space of the negotiation, but instead of arbitrating a final agreement, it allows the agents themselves to ratify the final agreement.

We present two option pricing models, both different from the classical Black-Scholes-Merton model. The first model, suggested by Heston, considers the case where the asset price volatility is stochastic. For this model we study the asset price process and give in detail the derivation of the European call option price process. The second model, suggested by Brody-Hughston-Macrina, describes the observation of certain information about the claim perturbed by a noise represented by a Brownian bridge. Here we also study in detail the properties of this noisy information process and give the derivations of both asset price dynamics and the European call option price process.

This thesis consists of five scientific papers dealing with equations related to the optimal switching problem, mainly backward stochastic differential equations and variational inequalities. Besides the scientific papers, the thesis contains an introduction to the optimal switching problem and a brief outline of possible topics for future research. Paper I concerns systems of variational inequalities with operators of Kolmogorov type. We prove a comparison principle for sub- and supersolutions and prove the existence of a solution as the limit of solutions to iteratively defined interconnected obstacle problems. Furthermore, we use regularity results for a related obstacle problem to prove Hölder continuity of this solution. Paper II deals with systems of variational inequalities in which the operator is of non-local type. By using a maximum principle adapted to this non-local setting we prove a comparison principle for sub- and supersolutions. Existence of a solution is proved using this comparison principle and Perron's method. In Paper III we study backward stochastic differential equations in which the solutions are reflected to stay inside a time-dependent domain. The driving process is of Wiener-Poisson type, allowing for jumps. By a penalization technique we prove existence of a solution when the bounding domain has convex and non-increasing time slices. Uniqueness is proved by an argument based on Ito's formula. Paper IV and Paper V concern optimal switching problems under incomplete information. In Paper IV, we construct an entirely simulation based numerical scheme to calculate the value function of such problems. We prove the convergence of this scheme when the underlying processes fit into the framework of Kalman-Bucy filtering. Paper V contains a deterministic approach to incomplete information optimal switching problems. We study a simplistic setting and show that the problem can be reduced to a full information optimal switching problem. Furthermore, we prove that the value of information is positive and that the value function under incomplete information converges to that under full information when the noise in the observation vanishes.

Diss. Stockholm : Handelshögskolan, 2005.

Submitted by Nathan Canen (njcanen@hotmail.com) on 2013-06-24T15:19:50Z No. of bitstreams: 1 canen bibdigital.pdf: 1062902 bytes, checksum: fa161af0125b4866558e27daf2adf766 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2013-06-27T11:38:59Z (GMT) No. of bitstreams: 1 canen bibdigital.pdf: 1062902 bytes, checksum: fa161af0125b4866558e27daf2adf766 (MD5) / Made available in DSpace on 2013-06-27T11:39:18Z (GMT). No. of bitstreams: 1 canen bibdigital.pdf: 1062902 bytes, checksum: fa161af0125b4866558e27daf2adf766 (MD5) Previous issue date: 2013-06-05 / How do economic shocks affect the behaviour of elections in democracies? Using U.S. Congress electoral data, I test whether sudden shocks affect unequally incumbent par- ties and opponents. This is identified through, among other procedures, a regression discontinuity design. I consider possible theoretical channels for this effect, where cit- izens cannot perfectly observe whether their lack of public goods is due to an adverse shock, or due to private consumption by a politician. I find that, with observable shocks close to the election, there is no effect. Empirical evidence is consistent with the theory. / Como choques econômicos afetam eleições em democracias? Usando dados eleitorais do Congresso dos Estados Unidos, eu testo se choques adversos podem afetar desigualmente partidos incumbentes e oponentes. Esse efeito é identificado, entre vários procedimentos, por uma regressão em descontinuidade. Eu considero possibilidades teóricas para esse efeito, quando cidadãos não conseguem observar perfeitamente se a falta de bens públicos é devido a um choque adverso, ou a consumo privado do político. Quando o choque é observável, não há efeito; enquanto se não fosse, haveria. As evidências empíricas são consistentes com a teoria.

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.

[pt] Este trabalho propõe um modelo de implementação de um leilão bidimensional para concessões de serviços públicos. O desenho do leilão é feito pelo governo através de uma regra de pontuação quase-linear que valora o preço cobrado e o tempo para iniciar a prestação de serviços. Este modelo aplica-se ao conjunto de serviços públicos que geram grandes benefícios quando começam a ser prestado em uma data limite reduzida. Os potenciais compradores possuem informação privada sobre seus custos de produção e redução do tempo. A regra de pontuação reduz a dimensionalidade dos lances tornando-os unidimensionais para os participantes, o maior lance resulta em uma obrigação contratual ao vencedor. O modelo auxilia na elaboração do design do leilão de forma a maximizar as preferências do governo dado o comportamento estratégico dos compradores. / [en] In this thesis we propose a model for a two-dimensional auction of public service concession agreements. The government design of the auction involves an almost linear scoring rule that evaluates the price charged and the time to start providing the services. The model applies to the public services that improve social welfare by reducing the delivery time of services. Suppliers have private information about their costs and time reduction offer. The proposed scoring rule of each supplier reduces the dimensionality of the bids submitted to a single dimension. The winner is committed to his bid and obliges to provide the required services. The model assists in preparing the design of the auction in order to maximize the preferences of the government given to the strategic behavior of buyers.