Basic equations, theory and principle of computational stock market (III)—basic theories

Abstract

By basic equations, two basic theories are presented: 1. Theory of stock' s value υ* (t) = υ*(0) exp(ar*₂ t); 2. Theory of conservation of stock' s energy. Let stock' s energy ϕ be defined as a quadratic function of stock' s price υ and its derivative$\dot v,\phi = {\rm A}v^2 + Bv\dot v + C\dot v^2 + Dv$, under the constraint of basic equation, the problem was reduced to a problem of constrained optimization along optimal path. Using Lagrange multiplier and Euler equation of variation method, it can be proved that ϕ keeps conservation for any υ,$\dot v$. The application of these equations and theories on judgement and analysis of tendency of stock market are given, and the judgement is checked to be correct by the recorded tendency of Shenzhen and Shanghai stock markets.