经济物理的基本问题.ppt

Principle of Large Numbers for Positive Variables SN=X1+X2+ . . . . . . +XN Observed relative deviation of US real GDP is 20 times larger than Lucas model（Chen 2002)！ Relative Deviation (RD) and the Implied Number (N*) from Empirical Observation Relative deviation Implied number Large Numbers in US Economy Weak microfoundations in labor and producer market The observed implied numbers predicted by the Lucas model is 400~ 500 times smaller (RD is 20 times larger ) than in US real economy. Possible microfoundations in financial markets and industrial organization not in labor or producer market Implication Three layer structure (micro, meso, macro) rather than two layer structure (micro, macro) in economies Implications from the Failure of Lucas Model of Microfoundations Roots of persistent business cycles: Financial intermediates and industrial organization From two layer model (micro-macro) Three layer model (micro-meso-macro) Nature of macro fluctuations social movements Stable RD in US Macro Indexesobserved under HP filter RD Behavior for Stochastic Models Random walk is damping over time Brownian motion is exploding over time Only the Birth-death process is stable in time, which is a statistical model of endogenous fluctuations Economic diagnosis 经济危机的诊断和预警生灭过程的含时转移概率 理解危机的不同途径： Fat tail distribution (Levy, fractal Brownian motion, power law), regime switch between calm and turbulent market 高阶矩，生灭过程的主方程，与时间变化的转移概率 ? Linear (BS) Empirical (SP 500) Transition Probability in Birth-Death Process from SP data (Tang Chen 2010) Higher Moment Deviations (=System Risk) during Crisis (4-5th Moments are 1000 times larger than 2nd Moment Failure of Portforlio Diversification) Source of Financial Instability：Nonlinear Trend Higher Moments in Birth-Death Process Option pricing model based on nonlinear birth-death process Stability condition： Under stability: finite first second moment 》Ito 》construct arbitrage portfolio 》Black-S