Rational Addictive Behavior under Uncertainty

We develop a new model of addictive behavior that takes as a starting point the classic rational addiction model of Becker and Murphy, but incorporates uncertainty. We model uncertainty through the Wiener stochastic process. This process captures both random events such as anxiety, tensions and environmental cues which can precipitate and exacerbate addictions, and those sober and thought-provoking episodes that discourage addictions. We derive closed-form expressions for optimal (and expected optimal) addictive consumption and capital trajectories and examine their global and local properties. Our theory provides plausible explanations of several important patterns of addictive behavior, and has novel implications for addiction control policy.