Optimal Contract for a Fund Manager with Capital Injections and Endogenous Trading Constraints

Nadtochiy, Sergey; Zariphopoulou, Thaleia

doi:10.1137/18m1172867

Cited by 7 publications

(2 citation statements)

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“…Related notions were developed and studied in Henderson and Hobson (2007) and El Karoui and Mohamed (2013); see also Bernard and Kwak (2016) and Choulli and Ma (2017). More recently, they have also been considered in discrete-time by Angoshtari et al (2020) and Strub and Zhou (2020), applied to problems arising in insurance by Chong (2019), extended to settings with model ambiguity in Källblad et al (2018) and Chong and Liang (2018), and applied to optimal contract theory in Nadtochiy and Zariphopoulou (2019). The main challenge to study forward performance processes is that the associated stochastic optimization problems are, in general, ill-posed as one assigns an initial utility and not a terminal one.…”

Section: Introductionmentioning

confidence: 99%

“…(2020) and Strub and Zhou (2020), applied to problems arising in insurance by Chong (2019), extended to settings with model ambiguity in Källblad et al. (2018) and Chong and Liang (2018), and applied to optimal contract theory in Nadtochiy and Zariphopoulou (2019). The main challenge to study forward performance processes is that the associated stochastic optimization problems are, in general, ill‐posed as one assigns an initial utility and not a terminal one.…”

Section: Introductionmentioning

confidence: 99%

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Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion

Strub

Zariphopoulou

2021

Mathematical Finance

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We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the timeconsistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, 'distorted' measure and a related market. We then build a striking correspondence between the forward

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