2020/12/03 by Bahman Angoshtari, Erhan Bayraktar, Angoshtari, Bahman +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Energy · #4902 #9101 #91G10 #Decision-Making and Behavioral Economics #Economic theories and models #Energy, Environment, and Transportation Policies #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM)
paper · pdf · doi:10.48550/arxiv.2012.02277
openalex publication_date 2020/12/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We formulate and solve a deterministic optimal consumption problem to maximize the discounted CRRA utility of an individual's consumption-to-habit process assuming she only invests in a riskless market and that she is unwilling to consume at a rate below a certain proportion α∈(0,1] of her consumption habit. Increasing α, increases the degree of addictiveness of habit formation, with α=0 (respectively, α=1) corresponding to non-addictive (respectively, completely addictive) model. We derive the optimal consumption policies explicitly in terms of the solution of a nonlinear free-boundary problem, which we analyze in detail. Impatient individuals (or, equivalently, those with more addictive habits) always consume above the minimum rate; thus, they eventually attain the minimum wealth-to-habit ratio. Patient individuals (or, equivalently, those with less addictive habits) consume at the minimum rate if their wealth-to-habit ratio is below a threshold, and above it otherwise. By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level. Additionally, we prove that the optimal consumption path is hump-shaped if the initial wealth-to-habit ratio is either: (1) larger than a high threshold; or (2) below a low threshold and the agent is more risk seeking (that is, less risk averse). Thus, we provide a simple explanation for the consumption hump observed by various empirical studies.