Asset trading under non-classical ambiguity (original) (raw)

Asset trading under non-classical ambiguity and heterogeneous beliefs

Physica A: Statistical Mechanics and its Applications

We propose discrete time asset trading framework based on quantum probability formalism that represents well the ambiguity of agents in respect to the fundamental values and price states of the traded assets. Divergence of beliefs alike classical finance frameworks (e.g. works by Harrison and Kreps, 1978 [24]; Scheinkman and Xiong, 2003 [50]) produces different expectations of agents about the future price distribution of the traded risky asset. The model accounts for the

Ambiguity in asset markets: theory and experiment

Review of Financial …, 2010

This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In particular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross-section of portfolio choices, a wider range of state price/probability ratios and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are infra-marginal: ambiguity averse investors have an indirect effect on prices because they change the per-capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the "value effect" in historical data.

Heterogeneous Beliefs and Asset Pricing in Discrete Time

RePEc: Research Papers in Economics, 2006

The aim of the paper is to analyze the impact of heterogeneous beliefs in an otherwise standard competitive complete markets discrete time economy. The construction of a consensus belief, as well as a consensus consumer are shown to be valid modulo a predictable aggregation bias, which takes the form of a discount factor. We use our construction of a consensus consumer to investigate the impact of beliefs heterogeneity on the CCAPM and on the expression of the risk free rate. We focus on the pessimism/doubt of the consensus consumer and we study their impact on the equilibrium characteristics (market price of risk, risk free rate). We …nally analyze how pessimism and doubt at the aggregate level result from pessimism and doubt at the individual level.

Trading heterogeneity under information uncertainty

Journal of Economic Behavior & Organization, 2016

Instead of heuristical heterogeneity assumption in the current heterogeneous agent models (HAMs), we derive the trading heterogeneity by introducing information uncertainty about the fundamental value to a HAM. Conditional on their private information about the fundamental value, agents choose different trading strategies when optimizing their expected utilities. This provides a microfoundation to heterogeneity and switching behavior of agents. We show that the HAM with trading heterogeneity originating from the incomplete information performs equally well, if not better than existing HAMs, in generating bubbles, crashes, and mean-reverting prices. The simulated time series matches with the S&P 500 in terms of power law distribution in returns, volatility clustering and long memory in volatility.

Speculative trading with rational beliefs and endogenous uncertainty

Economic Theory, 2003

This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are "rational" in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions.

Ambiguity and asset prices: an experimental perspective

2006

Most of the economics and finance literature assumes that individual agents obey the Savage axioms; that is, they maximize expected utility according to subjective priors. However, Knight, Ellsberg and others argue that individual agents distinguish between risk (known probabilities) and uncertainty, or ambiguity (unknown probabilities), and that individual agents may display aversion to ambiguity, just as they display aversion to risk. This paper studies the impact of ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitude toward ambiguity is heterogeneous in the population, just as attitude toward risk is heterogeneous in the population, but that heterogeneity in attitude toward ambiguity has different implications than heterogeneity in attitude toward risk: agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This leads to a wider range of state price densities and to potential reversals of ranking of state price densities. Experiments confirm the theoretical predictions.

A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs

Computational Economics, 2010

This paper presents a new stochastic model of asset pricing, based on agents with heterogeneous beliefs. Forecasting rules of all agents are characterized by a stochastic term that works as an agent-based time dependent weight of the conditional expectation of the fundamental. Since we consider the presence of an imitative behavior between agents, these weights depend stochastically on the type-distribution of agents. The resulting dynamical system is firstly analyzed in a deterministic framework. Starting from the results obtained in the deterministic case, the model is lastly explored by reintroducing randomness. The deterministic study aims at providing the existence of a region in the parameters plane where the unique possible dynamics is the convergence to a steady state, while complexity is exhibited outside such region. This region is also analyzed by reintroducing stochasticity and we provide an explicit formula for its probability measure. Our findings are in agreement with the economic meaning of the parameters. Finally, we propose a bayesian analysis, in order to explore the distribution of the adjustment term of the proportion of agents.

Prices and allocations in asset markets with heterogeneous attitudes towards ambiguity

Review of Financial …, 2007

This paper studies the impact of ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitude toward ambiguity is heterogeneous in the population, just as attitude toward risk is heterogeneous in the population, but that heterogeneity in attitude toward ambiguity has different implications than heterogeneity in attitude toward risk. Specifically, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This leads to a wider range of state price densities and to potential reversals of ranking of state price-probability ratios relative to aggregate wealth. In addition, the distribution of holdings will have a new mode, with highly ambiguity averse agents holding securities with ambiguous payoffs in equal proportions. Under pure risk, the distribution of holdings has a single mode equal to the market portfolio weight. Experiments confirm the theoretical predictions. While price patterns often look little different from those under pure risk, portfolio choices display strong effects from the presence of ambiguity. The experiments also suggest a positive correlation between risk aversion and ambiguity aversion, which may explain the "value effect" in field data. † We are grateful for comments to seminar audiences at CIRANO, U.C. Irvine, Kobe University, Collegio

Heterogeneous beliefs and asset pricing in discrete time: An analysis of pessimism and doubt

Journal of Economic Dynamics and Control, 2006

Asset trading under non-classical ambiguity (original) (raw)

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