This paper presents a survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection theories. We present the relevant techniques underlying homotopy algorithms. We give detailed expositions of the Lemke-Howson algorithm a...

We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between t...

Constraints on downside risk, measured by shortfall probability, expected shortfall, semi-variance etc., lead to optimal asset allocations which differ from the meanvariance optimum. The resulting optimization problem can become quite complex as it exhibits multiple local extrema and discontinuities, in particular if we also introduce constraints restricting the trading variables to integers, c...

Using a result in Angelini and Herzel (2009a), we measure, in terms of variance, the cost of hedging a contingent claim when the hedging portfolio is re-balanced at a discrete set of dates. We analyze the dependence of the variance of the hedging error on the skewness and kurtosis as modeled by a Normal Inverse Gaussian model. We consider two types of strategies, the standard Black-Scholes Delt...

This paper compares two methodologies that have been used to understand the evolution of bargaining conventions. The first is the analytical approach that employs a standard learning dynamic and computes equilibria numerically. The second approach simulates an environment with a finite population of interacting agents. We compare these two approaches within the context of three variations on a ...

This paper concludes the study of transition paths in the continuous-time recombinant endogenous growth model by providing numerical methods to estimate the threshold initial value of capital (a Skiba-type point) above which the economy takes off toward sustained growth in the long run, while it is doomed to stagnation otherwise. The model is based on the setting first introduced by Tsur and Ze...

We consider counterparty risk for Credit Default Swaps (CDS) in presence of correlation between default of the counterparty and default of the CDS reference credit. Our approach is innovative in that, besides default correlation, which was taken into account in earlier approaches, we also model credit spread volatility. Stochastic intensity models are adopted for the default events, and default...

A large market economy has a huge number of degrees of freedom with weak microlevel coordination. The ‘implicit microfoundations’ approach considers this property of micro-level interactions to more strongly determine macro-level outcomes compared to the precise details of individual choice behavior; that is, the ‘particle’ nature of individuals dominates their ‘mechanical’ nature. So rather th...

Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method for Bayesian analysis of models with ill-behaved posterior distributions. In order to sample e ciently from such a distribution, a location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a MetropolisHastings algorithm is applied to sample direct...