  We introduce and study a mathematical model of an art collector. In our
model, the collector is a rational agent whose actions in the art market are
driven by two competing long-term objectives, namely sustainable financial
health and maintaining the collection. Mathematically, our model is a
two-dimensional random linear dynamical system with transformation matrix of a
peculiar type. In some examples we are able to show that within the Kelly-type
optimization paradigm, that is optimizing the system's Lyapunov exponent over a
set of policy parameters, the dilemma ``art or money" can be successfully
resolved, namely the optimal policy creates a coexistence equilibrium where the
value of both is increasing over the time.
