Optimal Intertemporal Consumption and Involuntary Memories of Consumption

Recent studies introduce the notion of treating autobiographical memories of past pleasurable experiences as assets and expanding the discounted utility model to include the utility of memories of past consumption. Recent studies in psychology have found that involuntary autobiographical memories are common in everyday life. This paper builds on these two strands in the literature by expanding the discounted utility model to include the utility of involuntary memories of past consumption. Optimal control theory is used to develop a continuous‐time optimal consumption model that takes into account the fact that consumption may generate involuntary memories that arrive at random times. The model is used in an in‐depth analysis of optimal consumption with memories. It is shown that memories shift consumption to earlier times. This effect gets weaker as the time horizon gets longer, and it vanishes entirely when the time horizon is infinite.