Quantitative Finance

In this paper, we present a simplified framework to represent competition, coordination and bargaining in fisheries when they operate under financial and technological constraints. Competition within constraints leads to a particular type of mathematical game in which the strategy choice by one player changes strategy set of the other. By studying the equilibria and bargaining space of this game when players maximize either profit or fishing capacity, we highlight that differences in financial constraints among players leads to a tougher play, with a reduced bargaining space as the least constrained player can readily exclude another from the competition. The exacerbating effects of constraints on competition are even stronger when players maximize capacity. We discuss the significance of our results for global ocean governance in a current context characterized by financialization and technological development. We suggest that in order to maximize the chances of fruitful negociations and aim towards a fair sharing of sea resources, it would be helpful to focus on leveling current differences in the constraints faced between competing fishing systems by supporting local financial systems and technological control, before implementing sophisticated economic tools.

This paper demonstrates the existence of a finite set of equilibria in the case of the indeterminacy of linear rational expectations models. The number of equilibria corresponds to the number of ways to select n eigenvectors among a larger set of eigenvectors related to stable eigenvalues. A finite set of equilibria is a substitute to continuous (uncountable) sets of sunspots equilibria, when the number of independent eigenvectors for each stable eigenvalue is equal to one.

We present a complete characterization of the classical transfer problem for an exchange economy with an arbitrary finite number of traders. Our method is geometric, using an equilibrium manifold developed by Debreu, Mas-Colell, and Balasko. We show that for a regular equilibrium the transfer problem arises if and only if the index at the equilibrium is ?? . This implies that the transfer problem does not happen if the equilibrium is Walras tatonnement stable. Our result generalizes Balasko's analogous result for an exchange economy with two traders.

Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for modelling stochastic interactions between agents, based on a herding process corrected by a price misalignment, and incorporating strong noise components in the agents' demand. The model's parameters are estimated using the method of simulated moments, where the moments reflect the basic properties of the daily returns of a stock market index. In addition, for the first time we apply a (parametric) bootstrap method in a setting where the switching between strategies is modelled using a discrete choice approach. As we demonstrate, the resulting dynamics replicate a rich set of the stylized facts of the daily financial data including: heavy tails, volatility clustering, long memory in absolute returns, as well as the absence of autocorrelation in raw returns, volatility-volume correlations, aggregate Gaussianity, concave price impact and extreme price events.

Resilience, the ability to recover from adverse events ("shocks"), is of fundamental importance to food security. This is especially true in poor countries, where basic needs are frequently threatened by economic, environmental, and health shocks. An empirically sound formalization of the concept of food security resilience, however, is lacking. Here we introduce a general framework for quantifying resilience based on a simple definition: a unit is resilient if (a) its long-term food security trend is not deteriorating and (b) the effects of shocks on this trend do not persist over time. Our approach can be applied to any food security variable for which high-frequency time-series data is available, can accommodate any unit of analysis (e.g., individuals, households, countries), and is especially useful in rapidly changing contexts wherein standard equilibrium-based economic models are ineffective. We illustrate our method with an analysis of per capita kilocalorie availability for 161 countries between 1961 and 2011. We find that resilient countries are not necessarily those that are characterized by high levels or less volatile fluctuations of kilocalorie intake. Accordingly, food security policies and programs will need to be tailored not only to welfare levels at any one time, but also to long-run welfare dynamics.

Mutually exclusive decisions have been studied for decades. Many well-known decision theories have been defined to help people either to make rational decisions or to interpret people's behaviors, such as expected utility theory, regret theory, prospect theory, and so on. The paper argues that none of these decision theories are designed to provide practical, normative and quantitative approaches for multiple mutually exclusive decisions. Different decision-makers should naturally make different choices for the same decision question, as they have different understandings and feelings on the same possible outcomes.The author tries to capture the different understandings and feelings from different decision-makers, and model them into a quantitative decision evaluation process, which everyone could benefit from. The basic elements in classic expected utility theory are kept in the new decision theory, but the influences from mutually exclusive decisions will also be modeled into the evaluation process. This may sound like regret theory, but the new approach is designed to fit multiple mutually exclusive decision scenarios, and it does not require a definition of probability weighting function. The new theory is designed to be simple and straightforward to use, and the results are expected to be rational for each decision-maker.

We propose a simple dynamical model of wealth evolution. The invariant distributions are of Pareto type and are dynamically stable as conjectured by Pareto.

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (1960, 1972) and Koopmans et al. (1964) with subsequent contributions by several other authors, including Bleichrodt et al. (2008). The papers by Hayashi (2003) and Olea and Strzalecki (2014) axiomatize quasi-hyperbolic discounting. The main contribution of this paper is to provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (1982) and Harvey (1986), we show that Anscombe and Aumann's (1963) version of Subjective Expected Utility theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.

Do boundedly rational players learn to choose equilibrium strategies as they play a game repeatedly? A large literature in behavioral game theory has proposed and experimentally tested various learning algorithms, but a comparative analysis of their equilibrium convergence properties is lacking. In this paper we analyze Experience-Weighted Attraction (EWA), which generalizes fictitious play, best reply dynamics, reinforcement learning and also replicator dynamics. We provide a comprehensive analytical characterization of the asymptotic behavior of EWA learning in 2?2 games. We recover some well-known results in the limiting cases in which EWA reduces to the learning rules that it generalizes, but also obtain new results for other parameterizations. For example, we show that in coordination games EWA may only converge to the Pareto-efficient equilibrium, never reaching the Pareto-inefficient one; that in Prisoner Dilemma games it may converge to fixed points of mutual cooperation; and that in Matching Pennies games it may fail to converge to any fixed point, following instead limit cycles or chaos.

We prove that the standard discrete-time accelerator equation cannot be considered as an exact discrete analog of the continuous-time accelerator equation. This leads to fact that the standard discrete-time macroeconomic models cannot be considered as exact discretization of the corresponding continuous-time models. As a result, the equations of the continuous and standard discrete models have different solutions and can predict the different behavior of the economy. In this paper, we propose a self-consistent discrete-time description of the economic accelerators that is based on the exact finite differences. For discrete-time approach, the model equations with exact differences have the same solutions as the corresponding continuous-time models and these discrete and continuous models describe the same behavior of the economy. Using the Harrod-Domar growth model as an example, we show that equations of the continuous-time model and the suggested exact discrete model have the same solutions and these models predict the same behavior of the economy.