  Using agent-based modelling, empirical evidence and physical ideas, such as
the energy function and the fact that the phase space must have twice the
dimension of the configuration space, we argue that the stochastic differential
equations which describe the motion of financial prices with respect to real
world probability measures should be of second order (and non-Markovian),
instead of first order models \`a la Bachelier--Samuelson. Our theoretical
result in stochastic dynamical systems shows that one cannot correctly reduce
second order models to first order models by simply forgetting about momenta.
We propose some simple second order models, including a stochastic constrained
n-oscillator, which can explain many market phenomena, such as boom-bust
cycles, stochastic quasi-periodic behavior, and "hot money" going from one
market sector to another.
