Optimal consumption with reference to past spending maximum

نویسندگان

چکیده

This paper studies the infinite-horizon optimal consumption problem with a path-dependent reference under exponential utility. The performance is measured by difference between nonnegative rate and fraction of historical maximum. running maximum process chosen as an auxiliary state process, hence value function depends on two variables. Hamilton–Jacobi–Bellman (HJB) equation can be heuristically expressed in piecewise manner across different regions to take into account all constraints. By employing dual transform smooth-fit principle, some thresholds wealth variable are derived such that classical solution HJB feedback investment strategies obtained closed form each region. A complete proof verification theorem provided, numerical examples presented illustrate financial implications.

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ژورنال

عنوان ژورنال: Finance and Stochastics

سال: 2022

ISSN: ['1432-1122', '0949-2984']

DOI: https://doi.org/10.1007/s00780-022-00475-w