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arXiv · 2403.15907

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

Reza Rastegar·Alex Roitershtein·Vadim Roytershteyn·Vijay Seetharam
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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.

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Reza Rastegar, Alex Roitershtein, Vadim Roytershteyn, Vijay Seetharam. 2024-03-23. Balancing art and money in pursuit of a Kelly-type optimality. https://arxiv.org/abs/2403.15907

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