Wealth and price distribution by diffusive approximation in a repeated prediction market

The approximate agents’ wealth and price invariant densities of a repeated prediction market model is derived using the Fokker–Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct

Long-run heterogeneity in an exchange economy with fixed-mix traders

We consider an exchange economy where agents have heterogeneous beliefs and assets are long-lived, and investigate the coupled dynamics of asset prices and agentsâ wealth. We assume that agents hold fixed-mix portfolios and invest on each asset proportionally to its expected dividends. We prove the existence and uniqueness of a sequence of arbitrage-free market equilibrium prices and provide sufficient conditions for an agent, or a group of agents, to survive or dominate. Our main finding is that long-run coexistence of agents with heterogeneous beliefs, leading to asset prices endogenous fluctuations, is a generic outcome of the market selection process

Innovation, Finance, and Economic Growth : an agent-based model

This paper extends the endogenous-growth agent-based model in Fagiolo and Dosi (2003) to study the financegrowth nexus. We explore industries where firms produce a homogeneous good using existing technologies, perform R&D activities to introduce new techniques, and imitate the most productive practices. Unlike the original model, we assume that both exploration and imitation require resources provided by banks, which pool agent savings and finance new projects via loans. We find that banking activity has a positive impact on growth. However, excessive financialization can hamper growth. In- deed, we find a significant and robust inverted-U shaped relation between financial depth and growth. Overall, our results stress the fundamental (and still poorly understood) role played by innovation in the finance-growth nex

Momentum and Reversal in a Financial Market with Persistent Heterogeneity

This paper investigates whether short-term momentum and long-term reversal may emerge from the wealth reallocation process taking place in speculative markets. We assume that there are two classes of investors who trade long-lived assets by holding constantly rebalanced portfolios based on their beliefs. Provided beliefs, and thus portfolios, are sufficiently diversified, all investors survive in the long-run and, due to waves of mispricing, the resulting equilibrium returns exhibit long-term reversal. If, moreover, asset dividends are positively correlated, investors’ profitable trades become positively correlated too, thus generating short-term momentum in equilibrium returns. We use the model to replicate the performance of the Winners and Losers portfolios highlighted by the empirical literature and to provide insights on how to improve upon them. Finally, we show that dividend positive autocorrelation is positively related to momentum and negatively related to reversal while diversity of beliefs is positively related to both momentum and reversa

Rationality and Asset Prices under Belief Heterogeneity

In this paper I study the relationship between rationality and asset prices when agents have heterogeneous and incorrect beliefs about future events. Using the fully rational pricing as a benchmark, I show that when agents behave according to the Subjective Generalized Kelly rule (Bottazzi et al., 2017), which is not optimal under agents’ beliefs, the long-run pricing performance is at least as good as the one emerging from an economy where agents maximize their preferences under rational price expectations. Indeed, there exist generic cases in which expected long-run prices of the Subjective Generalized Kelly economy approximate better the rational pricing than those attained by the utility maximizers economy. Moreover in the limit of agents having a discount factor equal to one the prices of the Subjective Generalized Kelly economy converge to those of the fully rational economy. Hence the fact that agents use non-optimal (heuristic) decision rules may correct for biases in beliefs and, as a consequence, improve the pricing performance of the economy

Rationality and asset prices under belief heterogeneity

In this paper I study the relationship between rationality and asset prices when agents have heterogeneous and incorrect beliefs about future events. Using as a benchmark the pricing derived under rational expectations (fully rational pricing), I compare the long-run pricing performance in terms of accuracy of an economy in which agents behave according to the Subjective Generalized Kelly rule (Bottazzi et al., Economic Theory, 66(2)407–447, 2018), which is not optimal under agents’ beliefs, with the one emerging from an economy where agents maximize logarithmic preferences under the same heterogeneous and incorrect beliefs. I find that, in the long-run, the Subjective Generalized Kelly economy prices either match those attained in the log-utility maximizers economy or, on average, approximate the fully rational pricing better. Moreover, in the limit of agents having a discount factor equal to one, asset prices of the Subjective Generalized Kelly economy converge to those of the fully rational economy. Hence the fact that agents use non-optimal (heuristic) decision rules may improve the pricing performance when agents have biased and heterogeneous beliefs. This is due to the evolutionary process of wealth reallocation taking place among agents, which lets non-optimality of rules compensate for biases in beliefs

Selection in incomplete markets and the CAPM portfolio rule

This paper studies whether, and to what extent, trading in an incomplete competitive market rewards the CAPM portfolio rule over alternative rules. We find that, if a mean-variance trader faces an agent who invests in each asset proportionally to expected relative payoffs, in the long-run only two scenarios are possible: either the mean-variance trader vanishes or both agents survive with fixed and constant wealth shares. In both cases, asymptotic prices are proportional to assets’ expected payoff, and the relation between prices and returns implied by the CAPM does not generally hold. Conversely, when a mean-variance trader faces a generic fixed-mix investor, several long-run outcomes are possible, such as dominance of one trader, survival of both, and generic path-dependency. We provide sufficient conditions to assess such outcomes. We find that the different outcomes can be effectively discussed in terms of the effective risk aversion of the trading strategies, as implied by their portfolio choices conditional on prevailing market prices. In general, a larger effective risk aversion constitutes a survival advantage

Far from the Madding Crowd: Collective Wisdom in Prediction Market

We investigate market selection and bet pricing in a simple Arrow security economy which we show is equivalent to the repeated prediction market models studied in the literature. We derive the condition for long run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of two fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities. Nor are they always nearer to the truth than the believes of all surviving agents. Moreover, we show that by adapting their beliefs to past prices, agents further decrease the agreement between market prices and true probabilities