An exact bandit model for the risk-volatility tradeoff

Max-Olivier Hongler; Renaud Rivier

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arXiv · 2311.13461

An exact bandit model for the risk-volatility tradeoff

Max-Olivier Hongler·Renaud Rivier

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Abstract

We revisit the two-armed bandit (TAB) problem where both arms are driven by diffusive stochastic processes with a common instantaneous reward. We focus on situations where the Radon-Nikodym derivative between the transition probability densities of the first arm with respect to the second is explicitly known. We calculate how the corresponding Gittins' indices behave under such a change of probability measure. This general framework is used to solve the optimal allocation of a TAB problem where the first arm is driven by a pure Brownian motion and the second is driven by a centered super-diffusive non-Gaussian process with variance quadratically growing in time. The probability spread due to the super-diffusion introduces an extra risk into the allocation problem. This drastically affects the optimal decision rule. Our modeling illustrates the interplay between the notions of risk and volatility.

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Max-Olivier Hongler, Renaud Rivier. 2023-11-22. An exact bandit model for the risk-volatility tradeoff. https://arxiv.org/abs/2311.13461

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