The Quant Finance Corner

Relativistic Memory in Finance

By Maurice Allais, American Economic Review, Vol. LVI, N°5, December 1966, pp. 1123-1156

In relation to physicial time, it is assumed that an instantaneous coefficient of forgetfulness Xsi(t), can be defined such that the effect of attrition of the memory of past events between T1 and T2 can be represented by the coefficient

$Exp\; -\; \int$_T1^T2 Xsi(u) du

which has an exponential form. A psychological time scale t' can then be defined such that

Xsi(t) dt = Xsi' dt',

where Xsi' is a constant; i.e., when measured in relation to psychological time, forgetfulness per unit of time is constant. In other words, by reference to this psychological time scale, memory is invariant.