By John H Jellett
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Extra info for An elementary treatise on calculus of variations (1850)
2006). More interestingly, the period of the fluctuation of the market price is twice that of the market fraction. t/ of the fundamentalists illustrated in Fig. 5c shows clearly the switching of agents’ trading strategies over the time. 2 0 25 50 75 100 t t τ=3 τ = 16 125 150 175 200 Fig. 4 (a) The corresponding bifurcation diagram of the market price with respect to ; and the market price for (b) D 3 and (c) D 16. Here k D 0:05, D 1; ˇf D 1:4; ˇc D 1:4; Á D 0:5; ˇ D 0:5, C D 0:02 and FN D 1. In the discrete-time Brock and Hommes framework, the rational routes to complicated price dynamics are characterized by the complicated bifurcations as the switching intensity ˇ increases.
Quantitative Finance, 1, 149–167. Hommes, C. (2006). Heterogeneous agent models in economics and finance. In L. L. ), Agent-based computational economics (Vol. 2 of handbook of computational economics, pp. 1109–1186). , & Stein, J. (2007). Disagreement and the stock market. Journal of Economic Perspectives, 21, 109–128. , & Napp, C. (2006). Heterogeneous beliefs and asset pricing in discrete time: An analysis of pessimism and doubt. Journal of Economic Dynamics and Control, 30, 1233–1260. , & Napp, C.
Their demand is positive if the last observed house price change is positive, and vice versa. However, the demand function of the chartists is S -shaped. Fundamentalists, in turn, still speculate on a fundamental price correction. Now the dynamics of the model is driven by a three-dimensional map, and there is only a unique fundamental steady state. Here we find analytical and numerical evidence of a Neimark-Sacker bifurcation, endogenous housing price dynamics and the coexistence of attractors.
An elementary treatise on calculus of variations (1850) by John H Jellett