"Behavioral Aspects of Arbitrageurs in Timing Games of Bubbles and Crashes"

We model a timing game of bubbles and crashes a la Abreu and Brunnermeier (2003), in which arbitrageurs compete with each other to beat the gun in a stock market. However, unlike Abreu and Brunnermeier, instead of assuming sequential awareness, the present paper assumes that with a small probability, each arbitrageur is behavioral and committed to ride the bubble at all times. We show that with incomplete information, even rational arbitrageurs are willing to ride the bubble. In particular, the bubble can persist for a long period as the unique Nash equilibrium outcome.

Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA

[EN] Despite the widespread use of the classical bicriteria Markowitz mean-variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean-variance methodology to obtain a mean-variance-sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of epsilon-dominance called ev-MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.This work was funded by "Ministerio de Economia y Competitividad" (Spain), research project RTI2018-096904B-I00, and "Conselleria de Educacion, Cultura y DeporteGeneralitat Valenciana" (Spain), research project AICO/2019/055Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Hilario Caballero, A.; Pla Santamaría, D.; Herrero Durá, JM. (2019). 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Behavioral Aspects of Arbitrageurs in Timing Games of Bubbles and Crashes

We model a timing game of bubbles and crashes a la Abreu and Brunnermeier (2003), in which arbitrageurs compete with each other to beat the gun in a stock market. However, unlike Abreu and Brunnermeier, instead of assuming sequential awareness,the present paper assumes that with a small probability, each arbitrageur is behavioral and committed to ride the bubble at all times. We show that with incomplete information, even rational arbitrageurs are willing to ride the bubble. In particular, the bubble can persist for a long period as the unique Nash equilibrium outcome.

Optimal Expectations

This paper introduces a tractable, structural model of subjective beliefs. Since agents that plan for the future care about expected future utility flows, current felicity can be increased by believing that better outcomes are more likely. On the other hand, expectations that are biased towards optimism worsen decision making, leading to poorer realized outcomes on average. Optimal expectations balance these forces by maximizing the total well-being of an agent over time. We apply our framework of optimal expectations to three different economic settings. In a portfolio choice problem, agents overestimate the return of their investment and underdiversify. In general equilibrium, agents' prior beliefs are endogenously heterogeneous, leading to gambling. Second, in a consumption-saving problem with stochastic income, agents are both overconfident and overoptimistic, and consume more than implied by rational beliefs early in life. Third, in choosing when to undertake a single task with an uncertain cost, agents exhibit several features of procrastination, including regret, intertemporal preference reversal, and a greater readiness to accept commitment.expectations formation, beliefs, overconfidence

The Densest k-Subhypergraph Problem

The Densest $k$-Subgraph (D$k$S) problem, and its corresponding minimization problem Smallest $p$-Edge Subgraph (S$p$ES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed that they do not an admit a subpolynomial approximation ratio (although the best known hardness results do not rule this out). In this paper we generalize both D$k$S and S$p$ES from graphs to hypergraphs. We consider the Densest $k$-Subhypergraph problem (given a hypergraph $(V, E)$, find a subset $W\subseteq V$ of $k$ vertices so as to maximize the number of hyperedges contained in $W$) and define the Minimum $p$-Union problem (given a hypergraph, choose $p$ of the hyperedges so as to minimize the number of vertices in their union). We focus in particular on the case where all hyperedges have size 3, as this is the simplest non-graph setting. For this case we provide an $O(n^{4(4-\sqrt{3})/13 + \epsilon}) \leq O(n^{0.697831+\epsilon})$-approximation (for arbitrary constant $\epsilon > 0$) for Densest $k$-Subhypergraph and an $\tilde O(n^{2/5})$-approximation for Minimum $p$-Union. We also give an $O(\sqrt{m})$-approximation for Minimum $p$-Union in general hypergraphs. Finally, we examine the interesting special case of interval hypergraphs (instances where the vertices are a subset of the natural numbers and the hyperedges are intervals of the line) and prove that both problems admit an exact polynomial time solution on these instances.Comment: 21 page

Market Liquidity and Funding Liquidity

We provide a model that links an asset's market liquidity - i.e., the ease with which it is traded - and traders' funding liquidity - i.e., the ease with which they can obtain funding. Traders provide market liquidity, and their ability to do so depends on their availability of funding. Conversely, traders' funding, i.e., their capital and the margins they are charged, depend on the assets' market liquidity. We show that, under certain conditions, margins are destabilizing and market liquidity and funding liquidity are mutually reinforcing, leading to liquidity spirals. The model explains the empirically documented features that market liquidity (i) can suddenly dry up, (ii) has commonality across securities, (iii) is related to volatility, (iv) is subject to "flight to quality", and (v) comoves with the market, and it provides new testable predictions.