The use of mixture distributions for modeling asset returns has a long history in finance. New methods of demonstrating support for the presence of mixtures in the multivariate case are provided. The use of a two-component multivariate normal mixture distribution, coupled with shrinkage via a quasi-Bayesian prior, is motivated, and shown to be numerically simple and reliable to estimate, unlike the majority of multivariate GARCH models in existence. Equally important, it provides a clear improvement over use of GARCH models feasible for use with a large number of assets, such as constant conditional correlation, dynamic conditional correlation, and their extensions, with respect to out-of-sample density forecasting. A generalization to a mixture of multivariate Laplace distributions is motivated via univariate and multivariate analysis of the data, and an expectation–maximization algorithm is developed for its estimation in conjunction with a quasi-Bayesian prior. It is shown to deliver significantly better forecasts than the mixed normal, with fast and numerically reliable estimation. Crucially, the distribution theory required for portfolio theory and risk assessment is developed.
In this paper we develop a Negishi approach to characterize recursive equilibria in stochastic models with overlapping generations. When competitive equilibria are Pareto-optimal, using Negishi-weights as a co-state variable has three major computational advantages over the standard approach of using the natural state: First, the endogenous state space is a unit simplex and thus easy to handle. Second, the number of unknown functions characterizing equilibrium dynamics is orders of magnitude smaller. Third, approximation errors have a compelling economic interpretation. Our main contribution is to show that the Negishi approach extends naturally to models with borrowing-constraints and incomplete financial markets where the welfare theorems fail. Many of the computational advantages carry over to this setting. We derive sufficient conditions for the existence of Markov equilibria in the complete markets model as well as for models with incomplete markets and borrowing constraints.
In this paper the optimal consumption strategy of an investor who owns a fixed sized risky project is studied. The cash flows generated by the risky project follow an arithmetic Brownian motion, and the investor earns interest on cash reserves. The short-rate may be stochastic, and the time horizon may be finite. This results in a family of Hamilton-Jacobi-Bellman variational inequalities that include PDEs whose solutions must be approximated numerically. To do so an finite element approximation and a time marching scheme are employed.
In this paper the decisions of a firm's manager, in terms of exposure to a profitable but risky technology, distribution of dividends and (costly) re-injection of cash to ward off bankruptcy are studied. The analysis of the manager's optimal choices is done via a value function whose state variable is the firm's current level of reserves. Contingent on whether proportional or fixed costs of reinvestment are considered, singular stochastic control or stochastic impulse control techniques are used.
Traditional models of sovereign debt assume that governments seek to maximize the long terminterests of their countries.We assume instead that governments borrow and default according to their own political interests. In particular they often have limited horizons and are reluctant to default strategically. This allows us to define a maximum sustainable debt to GDP ratio, and compute it as a function of the countrys fundamentals. We find that maximum sustainable debt varies a lot across countries, consistent with the notion of country specific debt (in)tolerance. Actual debt ratios are below their maximum sustainable levels, as governments seeking further terms in office fear debt-induced default that may jeopardize their prospects for reelection. The difference between actual and maximum sustainable debt ratios creates a "margin of safety" that allows governments to increase debt if necessary with little corresponding increase in default risk. The probability of default climbs precipitously once the margin of safety has been exhausted.
In this paper technology adoption behaviour under (regulatory) no-anticipation of new technology, and imperfect competition in a tradable permits scheme (rents market) is investigated. The inter-dependence between the incentive to adopt a new technology and the allowance price is explicitly modelled. A firm's longterm incentives to adopt a new technology depend on the future value of tradable permits (scarcity rents) and, ultimately, on the level of uncovered pollution emissions (permits demand) and the level of offered emission permits (permits supply)-both affected by the current technological status. In an imperfectly competitive permit market, the aggregate supply is the solution of a non-cooperative game that possesses a pure-strategy Nash equilibrium. It is shown that this condition is also satisfied when a price-support instrument, which is contingent on the adoption of the new technology, is introduced. This is done to foster the firms' long-term incentives to adopt new technologies. The impact of the price-support contract on the scarcity rent value and on the technology adoption behaviour is both theoretically and numerically examined: (i) it creates a floating price floor that can be interpreted as a minimum price guarantee; (ii) the higher the minimum price guarantee, the higher the aggregate level of adoption and the earlier the adoption of new technologies.
A large number of empirical studies find evidence for systematic deviations from the CAPM. The CAPM tends to understate the returns on low-beta stocks and overstate the returns on high-beta stocks, which means that the security market line is too steep. Other well-documented anomalies are the size premium and the value premium. The CAPM is a special case of the consumption-based CAPM. This study addresses the question whether the consumption-based CAPM with constant relative risk aversion preferences can explain CAPM-anomalies. An example of an economy with power utility and lognormal returns is examined that can be solved in closed form. The model leads to a security market line that is flatter than in the CAPM and generates a size and a value premium. The comparative statics suggest that cross-sectional anomalies and the equity premium puzzle are of a very similar nature.
The majority of academic economists share the view that a corporation should serve the exclusive interests of its shareholders (shareholder value maximization). This view is fi rmly grounded on the extension, by Arrow (1953) and Debreu (1959) of the two welfare theorems to production economies with uncertainty and complete markets. This paper considers a variant of the Arrow-Debreu model where uncertainty is endogenous: probabilities of productive outcomes depend on decisions made by fi rms. In that case, a competitive equilibrium with shareholder value maximizing fi rms (capitalist equilibrium) is never Pareto optimal. This is because endogenous uncertainty implies that firms exert externalities on their consumers and their employees. When rms are stakeholder oriented, in that their managers are instructed to maximize a weighted sum of their shareholder value and of their contributions to consumer and employee welfares, the new competitive equilibrium (stakeholder equilibrium) improves upon the capitalist equilibrium.
