Temporal and Spatial Turnpike-Type Results Under Forward Time-Monotone Performance Criteria

Geng, Tianran; Zariphopoulou, Thaleia

doi:10.48550/arxiv.1702.05649

Cited by 1 publication

(1 citation statement)

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“…The first example with a power utility function generalizes Corollary 6.4 in Angoshtari et al ( 2020). In the second example, the initial utility function corresponds to an inverse marginal function that is a sum of two power functions, see also He et al (2021) and Geng and Zariphopoulou (2017).…”

Section: Two Examplesmentioning

confidence: 99%

Predictable forward performance processes: Infrequent evaluation and applications to human‐machine interactions

Liang

Strub

Wang

2023

Mathematical Finance

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We study discrete‐time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we find that these processes are inherently myopic in the sense that optimal strategies do not make use of future model parameters even if these are known. Finally, we argue that predictable forward preferences are a viable framework to model human‐machine interactions occurring in automated trading or robo‐advising. For both applications, we determine an optimal interaction schedule of a human agent interacting infrequently with a machine that is in charge of trading.

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Section: Two Examplesmentioning

confidence: 99%