Public Congestion Network Situations, and Related Games

This paper analyzes congestion effects on network situations from a cooperative game theoretic perspective. In network situations players have to connect themselves to a source. Since we consider publicly available networks any group of players is allowed to use the entire network to establish their connection. We deal with the problem of finding an optimal network, the main focus of this paper is however to discuss the arising cost allocation problem. For this we introduce two different transferable utility cost games. For concave cost functions we use the direct cost game, where coalition costs are based on what a coalition can do in absence of other players. This paper however mainly discusses network situations with convex cost functions, which are analyzed by the use of the marginal cost game. In this game the cost of a coalition is defined as the additional cost it induces when it joins the complementary group of players. We prove that this game is concave. Furthermore, we define a cost allocation by means of three egalitarian principles, and show that this allocation is an element of the core of the marginal cost game. These results are extended to a class of continuous network situations and associated games.Congestion;network situations;cooperative games;public

Fall Back Equilibrium

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.strategic game;equilibrium refinement;blocked action;fall back equilibrium

Simulated maximum likelihood for general stochastic volatility models: a change of variable approach

Maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. Using a sequential change of variable framework, we are able to cast more general stochastic volatility models into a form appropriate for importance samplers based on the Laplace approximation. We apply the methodology to two example models, showing that efficient importance samplers can be constructed even for highly non-Gaussian latent processes such as square-root diffusions.Change of Variable; Heston Model; Laplace Importance Sampler; Simulated Maximum Likelihood; Stochastic Volatility

The SU(2) Skyrme model and anomaly

The SU(2) Skyrme model,expanding in the collective coordinates variables, gives rise to second-class constraints. Recently this system was embedded in a more general Abelian gauge theory using the BFFT Hamiltonian method. In this work we quantize this gauge theory computing the Noether current anomaly using for this two different methods: an operatorial Dirac first class formalism and the non-local BV quantization coupled with the Fujikawa regularization procedure.Comment: 6 pages, Revtex. Final version to be published in Physics Letters

Modelling interactive behaviour, and solution concepts

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Modelling interactive behaviour, and solution concepts.

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time

A new algorithm is developed to provide a simulated maximum likelihood estimation of the GARCH diffusion model of Nelson (1990) based on return data only. The method combines two accurate approximation procedures, namely, the polynomial expansion of Aït-Sahalia (2008) to approximate the transition probability density of return and volatility, and the Efficient Importance Sampler (EIS) of Richard and Zhang (2007) to integrate out the volatility. The first and second order terms in the polynomial expansion are used to generate a base-line importance density for an EIS algorithm. The higher order terms are included when evaluating the importance weights. Monte Carlo experiments show that the new method works well and the discretization error is well controlled by the polynomial expansion. In the empirical application, we fit the GARCH diffusion to equity data, perform diagnostics on the model fit, and test the finiteness of the importance weights.Ecient importance sampling; GARCH diusion model; Simulated Maximum likelihood; Stochastic volatility

Stimulated Maximum Likelihood Estimation of Continuous Time Stochastic Volatility Models

In this paper we develop and implement a method for maximum simulated likelihood estimation of the continuous time stochastic volatility model with the constant elasticity of volatility. The approach do not require observations on option prices nor volatility. To integrate out latent volatility from the joint density of return and volatility, a modified efficient importance sampling technique is used after the continuous time model is approximated using the Euler-Maruyama scheme. The Monte Carlo studies show that the method works well and the empirical applications illustrate usefulness of the method. Empirical results provide strong evidence against the Heston model.Efficient importance sampler; Constant elasticity of volatility

Simulated Maximum Likelihood Estimation for Latent Diffusion Models

In this paper a method is developed and implemented to provide the simulated maximum likelihood estimation of latent diffusions based on discrete data. The method is applicable to diffusions that either have latent elements in the state vector or are only observed at discrete time with a noise. Latent diffusions are very important in practical applications in nancial economics. The proposed approach synthesizes the closed form method of Aït-Sahalia (2008) and the ecient importance sampler of Richard and Zhang (2007). It does not require any inll observations to be introduced and hence is computationally tractable. The Monte Carlo study shows that the method works well in finite sample. The empirical applications illustrate usefulness of the method and find no evidence of infinite variance in the importance sampler.Closed-form approximation; Diusion Model; Ecient importance sampler