Stock Market and Motion of a Variable Mass Spring

TL;DR

This paper models stock market dynamics using a variable mass spring analogy, deriving log-periodic oscillations and connecting them to Tsallis statistics, offering a novel physical perspective on economic fluctuations.

Contribution

It introduces a spring-mass analogy with increasing mass to describe stock market behavior and links oscillatory patterns to non-extensive Tsallis entropy.

Findings

Derivation of log-periodic price oscillations.

Connection between demand-supply fluctuations and Tsallis q parameter.

Model predicts oscillatory behavior in commodity prices.

Abstract

We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637 (2000)]. The total system energy E_t is shown to be proportional to a decreasing time dependent spring constant k_t. This model allows to derive log-periodicity cos[log (t-t_{c})] on commodity prices and oscillations (surplus and shortages) in the level of stocks. We also made an attempt to connect these results to the Tsallis statistics parameter q based on a possible force-entropy correlation [Physica A 341, 165 (2004)] and find that the Tsallis second entropic term \sum_{i=1}^{W} p_i^{q}/(q-1) relates to the square of the demand (or supply) function.