The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

Foundations Of Statistics

Investor Psychology and Security Market Under- and Overreactions

This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.

/pdf/heterogeneous-agent-models-in-economics-and-finance-39c58xjv7z.pdf

Heterogeneous Agent Models in Economics and Finance

Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean.

Testing Continuous-Time Models of the Spot Interest Rate

It is shown that if the neuronal gains are small compared with the synaptic connection weights, then a bidirectional associative memory network with axonal signal transmission delays converges to the equilibria associated with exogenous inputs to the network. Both discrete and continuously distributed delays are considered; the asymptotic stability is global in the state space of neuronal activations and also is independent of the delays. >

/pdf/delay-independent-stability-in-bidirectional-associative-xbrppyasoi.pdf

Delay-independent stability in bidirectional associative memory networks

Stability in asymmetric Hopfield nets with transmission delays

Trade among individuals occurs either because tastes (risk aversion) differ, endowments differ, or beliefs differ. Utilisating the concept of :adaptively rational equilibrium" and a recent framework of Brock and Hommes [6, 7], this paper incorporates risk and learning schemes into a simple discounted present value asset price model with heterogeneous beliefs. Agents have different risk aversion coefficients and adapt their beliefs (about future returns) over time by choosing from different predictors or expectations functions, based upon their past performance as measured by realized profits. By using both bifurcation theory and numerical analysis, it is found that the dynamics of asset pricing is affected by the relative risk attitudes of different types of investors. It is also found that the external noise and learning schemes can significantly affect the dynamics. Compared with the findings of Brock and Hommes [7] on the dynamics caused by chage of the intensity of choice to switch predictors, it is found that many of their insights are robust to the generalizations considered; however, the resulting dynamical behavior is considerably enriched and exhibits some significant differences.

Heterogeneous Beliefs, Risks and Learning in a Simple Asset Pricing Model

Publisher Summary Although there might be agreement that the standard paradigm does not fully explain what is causing the evolution of speculative asset prices, there may be less agreement on where to start to build an improved paradigm. By and large, the view that has been adopted in the boundedly rational heterogeneous agent literature is to retain expected utility maximization as the goal of each agent but to allow the agents to have different risk preferences and different expectations, rather than the single homogeneous rational expectation, about future possible returns. The expectations differ since agents are assumed to have different information and beliefs. Thus the asset price modeling framework is based on the fact that trading is driven more by differences in expectations than by the random arrival of news events. Within this framework, a simple market of one risky asset and one risk-free asset, with agents having different expectations, is considered with two different types of utility functions and two different market-clearing mechanisms. The framework provides the basic elements and structure of the various models. The basic building blocks of this framework are portfolio optimization, agents' utility functions, the market-clearing mechanism, and expectations feedback.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1352111_code355571.pdf?abstractid=1352111

Heterogeneity, Market Mechanisms, and Asset Price Dynamics

Trade among individuals occurs either because tastes (risk aversion) differ, endowments differ, or beliefs differ. Utilising the concept of `adaptively rational equilibrium' and a recent framework of Brock and Hommes [6, 7] this paper incorporates risk and learning schemes into a simple discounted present value asset price model with heterogeneous beliefs. Agents have different risk aversion coefficients and adapt their beliefs (about future returns) over time by choosing from different predictors or expectations functions, based upon their past performance as measured by realized profits. By using both bifurcation theory and numerical analysis, it is found that the dynamics of asset pricing is affected by the relative risk attitudes of different types of investors. It is also found that the external noise and learning schemes can significantly affect the dynamics. Compared with the findings of Brock and Hommes [7] on the dynamics caused by change of the intensity of choice to switch predictors, it is found that many of their insights are robust to the generalizations considered: however, the resulting dynamical behavior is considerably enriched and exhibits some significant differences.

Xue-Zhong He

Papers

Delay-independent stability in bidirectional associative memory networks

Stability in asymmetric Hopfield nets with transmission delays

Heterogeneous Beliefs, Risks and Learning in a Simple Asset Pricing Model

Heterogeneity, Market Mechanisms, and Asset Price Dynamics

Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model