连续进化金融模型与全局渐进化稳定策略

本文运用达尔文生物进化论思想研究连续交易金融市场选择的动态变化及一般均衡规律。本文发现并证明了:金融资产“赢利”的充要条件是该资产相对股息大于相对股价;投资比例等于股息分发比例的简单混合策略是全局渐近进化稳定策略;在均衡条件下,对应的金融资产价格等于该资产股息占总股息的比例的数学期望;市场变异或金融创新是有效市场形成的动力;全局渐近进化稳定策略业绩可能在某些时候不是最好的,但只要其初始财富大于零,最终将控制市场上的所有财富,而简单混合策略,可能在某个时候业绩优良,然而,在市场存在全局渐近进化稳定策略的条件下,只要其初始财富份额小于1,最终控制的财富趋向于零,从而被市场所淘汰。

Continuous Time Evolutionary Financial Model and Globally Asymptotically Evolutionary Stable Strategies

This paper analyses dynamics and general equilibrium problem of continuous trading market selection by means of Darwin evolutionary ideas. In this setting there are lots of assets, each of which generates relative dividend exogenously and independently on present amount of wealth. Expected relative dividends are constant all the time and the asset prices are endogenously determined by supply and demand. There exist only two kinds of investors who invest according to fix-mix strategies. This paper shows that an asset gains profit if and only if its relative dividend is more than its relative price. The fix-mit in accord with expected relative dividends is globally asymptotically evolutionary stable and asset prices equal to expected relative dividends in a equilibrium. It is financial innovation that makes markets effective. Without financial innovation, the asset prices can be twisted into anything available. These conclusions contribute to natural selection hypothesis believed by Alchian(1950), Friedman(1953) and Fama(1965) and provide a rigorous analysis to the hypothesis as well.