Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

European option pricing model in a stochastic and fuzzy environment

The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.

Information Acquisition: Fundamental and Non-Fundamental

We present a parsimonious information acquisition model in which two types of traders can produce either fundamental or non-fundamental information.Fundamental information is related to asset liquidation value,whereas non-fundamental information is related to the noise caused by traders'sentiment.Opening access to non-fundamental information increases the coordination possibilities among sentiment-informed traders and can yield two equilibrium-displaying properties:substitutability and complementarity.We find that the dominated mass of one type of informed trader can attenuate their information advantage,resulting in low ex ante expected utility associated with such traders.We further find that there is a crowding-out effect in information acquisition between the two types of informed traders,which offers some significant insights in explaining why bubbles burst when market sentiment is dominant.

Illiquidity Comovement and Market Crisis

This paper presents a rational expectation equilibrium model to explore how the financial contagion occurs between the unlinked markets that do not share common fundamentals.In the proposed model,the authors assume two of the three risky assets share no common fundamental factors,but are connected by one intermediate asset via cross fundamentals.Through this channel,investors transmit fundamental risk from one asset to another by dint of the cross fundamentals.This mechanism causes liquidity comovement and subsequently becomes a source of market crisis:Through the contagion mechanism,an initial liquidity shock in one asset can result in a drop tendency in liquidity and price informativeness for another asset.Such comovement in liquidity offers a new explanation for idiosyncratic assets in financial contagion.

Heterogeneous Beliefs,Trading Volume,and Seemingly Emotional Stock Market Behavior

Various information types and rational learning methods have shown that heterogeneous belief changes in a rational expectation model can explain many empirical findings in stock markets, such as momentum, contrarians, and technical trading. The methods have also shown that momentum and price movements can coexist in an asset market with only rational agents. The purpose of this paper is to provide a rational economic theory to explain these phenomena. Results of a dynamic programming model with heterogeneous beliefs show that the dynamic interactions between information diffusion and belief changes create continuation and reversals. The duration and magnitude of momentum and price movements are associated with trading volume. Therefore, rational investors should incorporate price and volume information in their trading decisions.