Differentiability of the Value Function in Continuous–Time Economic Models

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous-time models of convex optimization arising in economics. We dispense with an interiority condition which is quite restrictive in constrained optimization and it is usually hard to check in applications. The differentiability of the value function is used to prove Bellman’s equation as well as the existence and continuity of the optimal feedback policy. We also establish uniqueness of the vector of dual variables under some conditions that rule out existence of asset pricing bubbles.Constrained optimization, value function, differentiability, envelope therem, duality theory.

Differentiability of the value function in continuous-time economic models.

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous—time models of convex optimization arising in economics. We dispense with an interioiity condition which is quite restrictive in constrained optimization and it is usually hard to check in applications. The differentiability of the value function is used to prove Bellman's equation as well as the existence and continuity of the optimal feedback policy. We also establish uniqueness of the vector of dual variables under some conditions that rule out existence of asset pricing bubbles.Constrained optimization; Value function; Differentiability; Envelope theorem; Duality theory;

SUSTAINABILITY AS INTERGENERATIONAL FAIRNESS

This paper presents an economic model of sustainability defined as intergenerational fairness. Assuming that intergenerational fairness is an obligation of each generation, a recursive optimization problem is obtained. The problem has the advantage that uncertainty can readily be incorporated in the model and it can be solved numerically for a wide range of specifications. The possibility of tradeoffs between efficiency and sustainability are discussed. Under plausible conditions, it is show that a sustainability obligation is met only if there is the expectations of economic growth.Agribusiness,

DYNAMIC PROGRAMMING: HAS ITS DAY ARRIVED?

Research Methods/ Statistical Methods,

MULTIPERIOD OPTIMIZATION: DYNAMIC PROGRAMMING VS. OPTIMAL CONTROL: DISCUSSION

Research Methods/ Statistical Methods,

A model of commodity money, with applications to Gresham's law and the debasement puzzle

We develop a model of commodity money and use it to analyze the following two questions motivated by issues in monetary history: What are the conditions under which Gresham's Law holds? And, what are the mechanics of a debasement (lowering the metallic content of coins)? The model contains light and heavy coins, imperfect information, and prices determined via bilateral bargaining. There are equilibria with neither, both, or only one type of coin in circulation. When both circulate, coins may trade by weight or by tale. We discuss the extent to which Gresham's Law holds in the various cases. Following a debasement, the quantity of reminting depends on the incentives offered by the sovereign. Equilibria exist with positive seigniorage and a mixture of old and new coins in circulation.Coinage ; Gresham's law

A model of commodity money, with applications to Gresham's Law and the debasement puzzle

We develop a model of commodity money and use it to analyze the following two questions motivated by issues in monetary history: What are the conditions under which Gresham's Law holds? And, what are the mechanics of a debasement (lowering the metallic content of coins)? The model contains light and heavy coins, imperfect information, and prices determined via bilateral bargaining. There are equilibria with neither, both, or only one type of coin in circulation. When both circulate, coins may trade by weight or by tale. We discuss the extent to which Gresham's Law holds in the various cases. Following a debasement, the quantity of reminting depends on the incentives oÃered by the sovereign. Equilibria exist with positive seigniorage and a mixture of old and new coins in circulation.Money ; Money theory ; Gresham's law

Optimization in semi-supervised classification of multivariate time series

Abstract. In this thesis, I study methods that classify time series in a semi-supervised manner. I compare the performance of models that assume independent and identically distributed observations against models that assume nearby observations to be dependent of each other. These models are evaluated on three real world time series data sets. In addition, I carefully go through the theory of mathematical optimization behind two successful algorithms used in this thesis: Support Vector Data Description and Dynamic Time Warping. For the algorithm Dynamic Time Warping, I provide a novel proof that is based on dynamic optimization. The experiments in this thesis suggest that the assumption of observations in time series to be independent and identically distributed may deteriorate the results of semi-supervised classification. The novel self-training method presented in this thesis called Peak Evaluation using Perceptually Important Points shows great performance on multivariate time series compared to the methods currently existing in literature. The feature subset selection of multivariate time series may improve classification performance, but finding a reliable unsupervised feature subset selection method remains an open question