Existence of an equilibrium for pure exchange economy with fuzzy preferences

This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent’s fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.

EXPECTATION-DRIVEN ASSET PRICE FLUCTUATIONS UNDER THE SPIRIT OF CAPITALISM HYPOTHESIS: THE ROLE OF HETEROGENEITY

In this paper, I study how heterogeneity amongst agents affects the occurrence of expectation-driven asset price fluctuations in a pure exchange economy à la Lucas, with infinitely lived households, under the hypothesis of spirit of capitalism (SOC). I consider heterogeneous households in terms of preferences, endowments, and initial wealth, and capture the SOC through preferences for wealth. Preferences for wealth are the key element of this paper in a twofold aspect. First, they explain the occurrence of asset price fluctuations driven by self-fulfilling changes in expectations. Second, heterogeneity in endowments affects asset price level and dynamics only if preferences are heterogeneous. For instance, if agents with the strongest SOC are also the rich in terms of endowments, heterogeneity in endowments heightens the asset price level in the long run and destabilizes by enlarging the range of parameter values for which expectation-driven asset price fluctuations occur.

HETEROGENEITY IN RISK PREFERENCES LEADS TO STOCHASTIC VOLATILITY

This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are heterogeneous in risk-preferences.

AN ECONOMIC PREMIUM PRINCIPLE UNDER THE DUAL THEORY OF THE SMOOTH AMBIGUITY MODEL

This study considers a pure exchange economy with insurance against ambiguous loss. Ambiguity preferences are represented by the dual theory of the smooth ambiguity model from Iwaki and Osaki (2014). The economic premium principle of Bühlmann (1980, 1984) is extended to ambiguity. We also perform some comparative statics and present sufficient conditions under which an increase in ambiguity aversion increases insurance demand and insurance premiums. Contrary to the result in Tsanakas and Christofides (2006), the optimal demand for insurance is not always comonotonic, because our model permits an economy comprising both ambiguity averse and ambiguity loving agents.