再论自适应赌注套期保值：风险和时间范围的考虑
Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon
摘要：
自适应下注对冲模型通常采用凯利关于最优赌博策略和信息的金融价值的著名著作中的见解。特别是，这样的模型寻求进化的解决方案，最大限度地提高长期平均增长率的谱系，即使在面对高度随机的增长轨迹。在这里，我们主张广泛偏离标准的方法，以更好地解释进化的偶然性。至关重要的是，我们将考虑波动性最小化，在有限的人口中的临时灭绝风险的动机，在有限的时间范围内的增长最大化的方法。我们发现，一个博弈论的竞争最优方法最好地捕捉这些额外的约束条件，并得出简单的健身支付函数和灭绝风险下的均衡解决方案。我们发现，对于最大的增长和最小的时间相对收益的对数最优策略是一个独特的纯策略对称均衡，进化的时间范围和低灭绝风险的鲁棒性不变。
英文摘要：
Models of adaptive bet-hedging commonly adopt 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 straightforward fitness payoff functions and extinction risks. We show that for both maximal growth and minimal time relative payoffs the log-optimal strategy is a unique pure-strategy symmetric equilibrium, invariant with evolutionary time horizon and robust to low extinction risks.
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