Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon
Omri Tal and Tat Dat Tran
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Submission date: 08. Apr. 2019 (revised version: April 2019)
Keywords and phrases: adaptive bet-hedging, Kelly gambling, game theory, growth optimal portfolio theory
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Standard approaches to modeling adaptive bet-hedging adopt important insights from Kelly’s famous work on optimal gambling strategies and the financial value of information. In particular, such models seek evolutionary solutions that maximize long term average growth rate of lineages, even in the face of highly stochastic growth trajectories. Here, we argue for extensive departures from the standard approach to better account for evolutionary contingencies. Crucially, we incorporate considerations of volatility minimization, motivated by interim extinction risk in finite populations, within a finite time horizon approach to growth maximization. We find that a game-theoretic competitive-optimality approach best captures these additional constraints, and derive the equilibria solutions under various fitness payoff functions.