Balancing art and money in pursuit of a Kelly-type optimality

TL;DR

This paper models an art collector's decision-making process balancing financial sustainability and collection preservation, demonstrating that optimal policies can lead to simultaneous growth in both art value and financial health.

Contribution

It introduces a novel mathematical model of an art collector's behavior using a two-dimensional dynamical system and applies Kelly-type optimization to resolve the art versus money dilemma.

Findings

Optimal policies can produce a coexistence equilibrium with increasing art and financial value.

The model shows that balancing art and money is achievable through specific policy choices.

The approach provides insights into long-term strategic decision-making in art collection management.

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.