Balancing art and money in pursuit of a Kelly-type optimality
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.15907
- arXiv:
- arXiv:2403.15907
- Bibcode:
- 2024arXiv240315907R
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Dynamical Systems;
- Mathematics - Optimization and Control;
- 91B74