Alex Roitershtein | Searcharxiv

arXiv2024

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

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.

math.PR↗

arXiv2022

On a characterization of exponential and double exponential distributions

Recently, G.~Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev's theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, obtain a similar characterization for the Laplace family of distributions.

math.PR↗