This article considers three standard asset pricing models with adaptive agents and stochastic dividends. The models only differ in the parameters to be estimated. We assume that only limited information is used to construct estimators. Therefore, parameters are not estimated consistently. More precisely, we assume that the parameters are estimated by exponential smoothing, where past parameters are down-weighted and the weight of recent observations does not decrease with time. This situation is familiar for applications in finance. Even if time series of volatile stocks or bonds are available for a long time, only recent data is used in the analysis. In this situation the prices do not converge and remain a random variable. This raises the question how to describe equilibrium behavior with stochastic prices. However, prices can reveal properties such as ergodicity, such that the law of the price process converges to a stationary law, which provides a natural and useful extension of the idea of equilibrium behavior of an economic system for a stochastic setup. It is this implied law of the price process that we investigate in this paper. We provide conditions for the ergodicity and analyze the stationary distribution. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Bounded Verification is an effective technique for finding subtle bugs in object-oriented programs. Given a program, its correctness specification and bounds on the input domain size, scope bounded checking translates bounded code segments into formulas in boolean logic and uses off the shelf satisfiability solvers to search for correctness violations. However, scalability is a key issue of the technique, since for non-trivial programs, the formulas are often complex and can choke the solvers. This thesis describes approaches which aim to scale scope bounded checking by utilizing syntactic and semantic information from the code to split a program into sub-programs which can be checked incrementally. It presents a thorough evaluation of the approaches and compares their performance with existing bounded verification techniques. Novel ideas for future work, specifically a specification slicing driven splitting approach, are proposed to further improve the scalability of bounded verification. / text

In many important economic situations, decision makers influence each other. The subject of game theory offers a mathematical framework to describe such strategic interaction. This dissertation focuses largely on helping to answering the question,"What will someone do in a particular strategic situation?" In order to do this, it is useful to interweave theory with experimentation. After all, observation of what people really do is a necessity when attempting to create models of what people really do. At the same time, theory can help significantly when formulating interesting hypotheses to test. The chapters in my dissertation illustrate this interweaving of theory and experiments.

This thesis concerns the relationship between bounded and controlled topology and in particular how these can be used to recognise which homotopy equivalences of reasonable topological spaces are homotopic to homeomorphisms. Let f : X → Y be a simplicial map of finite-dimensional locally finite simplicial complexes. Our first result is that f has contractible point inverses if and only if it is an ε- controlled homotopy equivalences for all ε > 0, if and only if f × id : X × R → Y × R is a homotopy equivalence bounded over the open cone O(Y +) of Pedersen and Weibel. The most difficult part, the passage from contractible point inverses to bounded over O(Y +) is proven using a new construction for a finite dimensional locally finite simplicial complex X, which we call the fundamental ε-subdivision cellulation X'ε. This whole approach can be generalised to algebra using geometric categories. In the second part of the thesis we again work over a finite-dimensional locally finite simplicial complex X, and use the X-controlled categories A*(X), A*(X) of Ranicki and Weiss (1990) together with the bounded categories CM(A) of Pedersen and Weibel (1989). Analogous to the barycentric subdivision of a simplicial complex, we define the algebraic barycentric subdivision of a chain complex over that simplicial complex. The main theorem of the thesis is then that a chain complex C is chain contractible in ( A*(X) A*(X) if and only if “C ¤ Z” 2 (A*(X × R) A*(X × R) is boundedly chain contractible when measured in O(X+) for a functor “ − Z” defined appropriately using algebraic subdivision. In the process we prove a squeezing result: a chain complex with a sufficiently small chain contraction has arbitrarily small chain contractions. The last part of the thesis draws some consequences for recognising homology manifolds in the homotopy types of Poincare Duality spaces. Squeezing tells us that a PL Poincare duality space with sufficiently controlled Poincare duality is necessarily a homology manifold and the main theorem tells us that a PL Poincare duality space X is a homology manifold if and only if X × R has bounded Poincare duality when measured in the open cone O(X+).

This thesis presents results concerning canonical extensions of bounded lattices and natural dualities for quasivarieties of default bilattices. Part I is dedicated to canonical extensions, while Part II focuses on natural duality for default bilattices. A canonical extension of a lattice-based algebra consists of a completion of the underlying lattice and extensions of the additional operations to the completion. Canonical extensions find rich application in providing an algebraic method for obtaining relational semantics for non-classical logics. Part I gives a new construction of the canonical extension of a bounded lattice. The construction is done via successive applications of functors and thus provides an elegant exposition of the fact that the canonical extension is functorial. Many existing constructions are described via representation and duality theorems. We demonstrate precisely how our new formulation relates to existing constructions as well as proving new results about complete lattices constructed from graphs. Part I ends with an analysis of the untopologised structures used in two methods of construction of canonical extensions of bounded lattices: the untopologised graphs used in our new construction, and the so-called `intermediate structure'. We provide sufficient conditions for the intermediate structure to be a lattice and, for the case of finite lattices, identify when the dual graph is not a minimal representation of the lattice. Part II applies techniques from natural duality theory to obtain dualities for quasivarieties of bilattices used in default logic. Bilattices are doubly-ordered algebraic structures which find application in reasoning about inconsistent and incomplete information. This account is the first attempt to provide dualities or representations when there is little interaction required between the two orders. Our investigations begin by using computer programs to calculate dualities for specific examples, before using purely theoretical techniques to obtain dualities for more general cases. The results obtained are extremely revealing, demonstrating how one of the lattice orders from the original algebra is encoded in the dual structure. We conclude Part II by describing a new class of default bilattices. These provide an alternative way of interpreting contradictory information. We obtain dualities for two newly-described quasivarieties and provide insights into how these dual structures relate to previously described classes of dual structures for bilattices.

Le résumé en français n'a pas été communiqué par l'auteur. / This paper studies firms’ disclosure decisions of product information in a duopoly setting, as well as the welfare implication of compulsory disclosure policy. I show that there is a problem of externality between the two firms: even if disclosure weakens price competition in the market and increases total industry profits, a firm could have incentive not to disclose product information because it decreases his market share. As a result, regulatory policy could increase total industry profits as it could rectify the problem of externality. Therefore, despite more information allows consumers to make a better choice between different alternatives, it might backfire as it could increase the average price in the market. I also present simple conditions on when providing more information could harm consumers, and when it will improve consumer welfare. This paper studies the information processing behavior of a decision maker (DM) who has limited information processing ability. More specifically, the DM can process only a subset of all available information. Before taking an action, he chooses whether to process or ignore signals about the state of the world which he receives sequentially. I show that at the optimum, the DM processes only signals which are strong enough, but will process a weaker signal if it confirms his existing strong belief or if it supports a much more desirable state of the world. This explains some phenomena which have been well documented in the psychology literature, such as preference for strong signals, confirmation bias for individuals with strong prior and wishful thinking. Moreover, I analyze how the Internet, and in general changes in information structures, affects the processing behavior of the DM. The results shed light on different issues in the information era, including polarization and media strategy. This paper studies experimentally whether confirmation bias arises when individuals are exposed to information overload, or equivalently have limited ability to perfectly update their belief with all available information. In our experiment, subjects have to form beliefs as they navigate a sequence of signals within a limited period of time. We compare belief formation under two settings, where the treatment setting imposes a larger information/cognitive load than the control setting. We find that subjects in the treatment setting exhibit a stronger confirmation bias than those in the control setting. Upon receiving a belief-challenging signal, subjects in the treatment group update their belief less than those in the control group. In contrast, upon receiving a belief-confirming signal, subjects update similarly in both settings. As a result, subjects in the treatment setting are also less likely to switch sides: once they believe that one state is more probable than another, they are less likely to switch even if they receive enough belief-challenging signals. Not only do these results show that the limited ability of information processing plays a role in the formation of confirmation bias, they also improve our understanding on the impact of information overload, for example on polarization.

Estudaremos aqui problemas de demonstrações em teorias fracas da Aritmética Limitada os teoremas sobre a infinidade dos primos e do princpio da casa dos pombos (limitado). Serão dadas soluções parciais para os dois problemas anteriores, além da demonstração que o grafco de x y = z tem definição 0 / We study here the problems of proving in weak theories of Bounded Arithmetic the theorems about the existence of arbitrarily large prime numbers and the (limited) pigeon hole principle. We will give partial solutions for the two foregoing problems, and the proof that the graphic of x y = z has a 0 definition

Lin, Jessey. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 79-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

This work presents the mathematical and computational aspects of a smooth dissipative particle dynamics with dynamic virtual particle allocation method (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains. The SDPD-DV method is realized with fluid particles, boundary particles and dynamically allocated virtual particles near solid boundaries. The physical domain in SDPD-DV contains external and internal solid boundaries, periodic inlets and outlets, and the fluid region. The solid boundaries of the domain are represented with boundary particles which have an assigned position, wall velocity, and temperature upon initialization. The fluid domain is discretized with fluid particles placed in a global index. The algorithm for nearest neighbor particle search is based on a combination of the linked-cell and Verlet-list approaches and utilizes large rectangular cells for computational efficiency. The density model of a fluid particle in the proximity of a solid boundary includes the contribution from the virtual particles in its truncated support domain. The thermodynamic properties of a virtual particle are identical to those of the corresponding fluid particle. A periodic boundary particle allocation method is used at periodic inlets and outlets. Models for the conservative and dissipative forces on a fluid particle in the proximity of a solid boundary are presented and include the contributions of the virtual particles in its truncated support domain. The integration of the fluid particle position and momentum equations is accomplished with an implementation of the velocity-Verlet algorithm. The integration is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. The integration of the entropy equation is based on the Runge-Kutta scheme. In isothermal simulations, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for compressible fluids. Sampling methods used for particle properties and transport coefficients in SDPD-DV are presented. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatio-temporal scales. The isothermal (without the entropy equation) SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes. Verification is achieved with SDPD-DV simulations of transient, Poiseuille, body-force driven flow of liquid water between plates separated. The velocity profiles from the SDPD-DV simulations are in very good agreement with analytical estimates and the field density fluctuation near solid boundaries is shown to be below 5%. Additional verification involves SDPD-DV simulations of transient, planar, Couette liquid water flow. The top plate is moving and separated from the bottom stationary plate. The numerical results are in very good agreement with the analytical solutions. Additional SDPD-DV verification is accomplished with the simulation of a body-force driven, low-Reynolds number flow of water over a cylinder of radius R=0.02m. The SDPD-DV field velocity and pressure are compared with those obtained by FLUENT. An extensive set of SDPD-DV simulations of liquid water and gaseous nitrogen in mesoscopic periodic domains is presented. For the SDPD-DV simulations of liquid water the mass of the fluid particles is varied between 1.24 and 3.3e-7 real molecular masses and their corresponding size is between 1.08 and 323 physical length scales. For SDPD-DV simulations of gaseous nitrogen the mass of the fluid particles is varied between 6.37e3and 6.37e6 real molecular masses and their corresponding size is between 2.2e2 and 2.2e3 physical length scales. The equilibrium states are obtained and show that the particle speeds scale inversely with particle mass (or size) and that the translational temperature is scale-free. The self-diffusion coefficient for liquid water is obtained through the mean-square displacement and the velocity auto-correlation methods for the range of fluid particle masses (or sizes) considered. Various analytical expressions for the self-diffusivity of the SDPD fluid are developed in analogy to the real fluid. The numerical results are in very good agreement with the SDPD-fluid analytical expressions. The numerical self-diffusivity is shown to be scale dependent. For fluid particles approaching asymptotically the mass of the real particle the self-diffusivity is shown to approach the experimental value. The Schmidt numbers obtained from the SDPD-DV simulations are within the range expected for liquid water. The SDPD-DV method (with entropy) is verified and validated with simulations with an extensive set of simulations of gaseous nitrogen in mesoscopic, periodic domains in equilibrium. The simulations of N2(g) are performed in rectangular domains. The self-diffusion coefficient for N2(g) at equilibrium states is obtained through the mean-square displacement for the range of fluid particle masses (or sizes) considered. The numerical self-diffusion is shown to be scale dependent. The simulations show that self-diffusion decreases with increasing mass ratio. For a given mass ratio, increasing the smoothing length, increases the self-diffusion coefficient. The shear viscosity obtained from SDPD-DV is shown to be scale free and in good agreement with the real value. We examine also the effects of timestep in SDPD-DV simulations by examining thermodynamic parameters at equilibrium. These results show that the time step can lead to a significant error depending on the fluid particle mass and smoothing length. Fluctuations in thermodynamic variables obtained from SDPD-DV are compared with analytical estimates. Additional verification involves SDPD-DV simulations of steady planar thermal Couette flow of N2(g). The top plate at temperature T1 =330K is moving at Vxw =30m/s and is separated by 10-4 m from the bottom stationary plate at T2=300K. The SDPD-DV velocity and temperature fields are in excellent agreement with those obtained by FLUENT.

Dans cette thèse nous étudions les algèbres des polynômes qui sont bornés sur un ensemble semi-algébrique non borné. Tout d'abord nous abordons le problème consistant à déterminer si un polynôme est borné sur un ensemble. Nous résolvons ce problème pour les polynômes à deux variables définis sur des ensembles semi-algébriques quelconques. Dans la section suivante nous donnons une méthode pour déterminer des générateurs de l'algèbre des polynômes bornés et ce pour une large classe de semi-algébriques du plan réel. Dans la section 3 nous établissons une relation entre les valeurs de bifurcation du complexifié d'un polynôme $f$ à deux variables et la stabilité de la famille d'algèbres des polynômes bornés sur les ensembles ${fle c}$. Dans la section 4 nous décrivons la structure de l'algèbre des polynômes bornés sur un certain type de sous-ensembles de $mathbb{R}^n$ avec $n$ arbitraire, que nous appelons tentacules pondérées. Nous donnons aussi une preuve géométrique du fait que l'algèbre d'un sous-ensemble non borné d'un ensemble algébrique propre n'est pas de type fini. Dans la section suivante nous établissons une correspondance entre les cônes convexes et les algèbres des ensembles obtenus par des inégalités sur des monômes appropriés. Enfin, nous démontrons une version du Positivstellensatz de Schmudgen pour les polynômes bornés sur un ensemble non compact. / The main topic of the thesis is a study of algebras of polynomials which are bounded on a given unbounded semialgebraic set. First we tackle the problem of deciding the boundedness of a polynomial on a set. We achieve it for polynomials in two variables for any semialgebraic set. We give also a method of finding generators of the algebra of bounded polynomials for a large class of semialgebraic subsets of the real plane. In Section 3 we have established a relation between bifurcation values of a complexification of polynomial $f$ in two variables and the family of algebras of bounded polynomials on the sets ${fle c}$. In section 4 we describe the algebras of bounded polynomials for subsets of $mathbb{R}^n$, where $n$ is arbitrary, which we call weighted tentacles. We also provide a geometric proof of the fact that for a unbounded subset of a proper algebraic set its algebra cannot be finitely generated. In the next section we establish a correspondence between convex cones and algebras of bounded polynomials on the sets described by monomial inequalities. At the end of this thesis we prove a version of Schmudgen's Positivstellensatz for bounded polynomials.