Simone Cavallero
Optimal growth in an uncertain environment.
Rel. Barbara Trivellato. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2023
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Abstract
Bet-hedging in biological phenomena is a well recognized process that can manifest itself as phenotypic switching: an individual has to choose the best strategy to adapt to a stochastic environment in order to maximize the growth rate of its own population. Fluctuations can lead to the extinction of the population itself, no matter how high the growth rate is. The same model can be applied to Kelly' s horse races studies, where the gambler has to choose the best strategy to maximize his payoff. We propose to add a definition of "risk" to Kelly's horse races model in order to map the phenotypic switching model into Kelly's one, taking into account the "bankruptcy" probability, that we want to minimize.
We end up considering the volatility as a measure of risk, as well as the probability of extinction itself and comparing the different definitions
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