Optimal Consumption with Reference to Past Spending Maximum

Shuoqing Deng, Xun Li, Huyen Pham and Xiang Yu

Papers from arXiv.org

Abstract: 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.

Date: 2020-06, Revised 2022-03
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2006.07223

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