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http://hdl.handle.net/10397/92467
Title: | Optimal consumption with reference to past spending maximum | Authors: | Deng, S Li, X Pham, H Yu, X |
Issue Date: | Apr-2022 | Source: | Finance and Stochastics, Apr. 2022, v. 26, no. 2, p. 217-266 | Abstract: | This paper studies the infinite-horizon optimal consumption problem 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 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. | Keywords: | Consumption running maximum Exponential utility Path-dependent reference Piecewise feedback control Verification theorem |
Publisher: | Springer | Journal: | Finance and Stochastics | ISSN: | 0949-2984 | EISSN: | 1432-1122 | DOI: | 10.1007/s00780-022-00475-w | Rights: | © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00780-022-00475-w. |
Appears in Collections: | Journal/Magazine Article |
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