Speculation with memory

摘要: This thesis considers asset price evolution in financial markets, deriving the dynamics from micro-economic considerations. In contrast to most models of speculative which Efficient Market Hypothesis is assumed valid, and thus process Markovian, we introduce dependence on past prices via action speculators endeavouring profit by extracting information history. Such speculators, called chartists, form a large portion agents markets. However, hitherto no satisfactory continuous time model their impact market behaviour has been developed. attempts close that gap. By modelling linear stochastic integro-differential equation making exogenous allowances for fluctuation agents’ participation levels periodicity present such show th t several properties markets can be qualitatively mimicked: relationship between heterogeneity fat-tailed returns distributions, autocorrelation term structure returns, volatility volume relative success chart speculators. Our outlines mechanisms bubbles or crashes arise, demonstrates certain types derivative pricing are robust violation Hypothesis. These applied results based new findings theory equations developed this thesis. We establish have unique, solutions whose paths same local topology as those Brownian Motion expressed terms resolvent related deterministic equation. By using techniques analysis (in particular Ito Calculus) equations, determine pathwise asymptotics, a.s. growth extrema asymptotic distributional character evolution.