Optimal Consumption with Reference to Past Spending Maximum
This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables. The Hamilton-Jacobi-Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account all constraints. By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that a classical solution to the HJB equation and the feedback optimal investment and consumption strategies can be obtained in closed form in each region. A complete proof of the verification theorem is provided, and numerical examples are presented to illustrate some financial implications.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Dynamic spending and portfolio decisions with a soft social norm
We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to tolerate occasional dips below it. We d…
Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences
This paper studies optimal consumption, investment, and healthcare spending under Epstein-Zin preferences. Given consumption and healthcare spending plans, Epstein-Zin utilities are defined over an agent's random lifetim…
Collaborative-Enhanced Prediction of Spending on Newly Downloaded Mobile Games under Consumption Uncertainty
With the surge in mobile gaming, accurately predicting user spending on newly downloaded games has become paramount for maximizing revenue. However, the inherently unpredictable nature of user behavior poses significant …
TANK meets Diaz-Alejandro: Household heterogeneity, non-homothetic preferences & policy design
This paper studies the role of households' heterogeneity in access to financial markets and the consumption of commodity goods in the transmission of foreign shocks. First, I use survey data from Uruguay to show that low…
Consumption-investment decisions with endogenous reference point and drawdown constraint
We propose a consumption-investment decision model where past consumption peak $h$ plays a crucial role. There are two important consumption levels: the lowest constrained level and a reference level, at which the risk a…