Rank-Dependent Utility and Risk Taking in Complete Markets

He, Xue Dong; Kouwenberg, Roy

doi:10.1137/16m1072516

Cited by 29 publications

(4 citation statements)

References 42 publications

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“…On the other hand, Theorem 4.1 does not impose any assumption on the distribution of R. In particular, Theorem 4.1 also holds when R follows a discrete distribution, such as a Bernoulli distribution. We refer to [16] for a similar result in a single-period complete market in which the RDU investor can trade a continuum of Arrow-Debreu securities.…”

Section: 1mentioning

confidence: 94%

“…Related to our work are [9], [24], [3], [12], [17] and [16], amongst others, who study the influence of probability weighting on optimal portfolio choice and asset pricing, either using RDU or cumulative prospect theory. The contribution of our work to this literature is that we explicitly focus on the question whether an increase in inverse S-shaped probability weighting leads to a lower or higher allocation to stocks, and under what conditions.…”

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confidence: 99%

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Inverse S-shaped probability weighting and its impact on investment

He¹,

Kouwenberg²

2018

MCRF

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In this paper we analyze how changes in inverse S-shaped probability weighting influence optimal portfolio choice in a rank-dependent utility model. We derive sufficient conditions for the existence of an optimal solution of the investment problem, and then define the notion of a more inverse S-shaped probability weighting function. We show that an increase in inverse S-shaped weighting typically leads to a lower allocation to the risky asset, regardless of whether the return distribution is skewed left or right, as long as it offers a non-negligible risk premium. Only for lottery stocks with poor expected returns and extremely positive skewness does an increase in inverse S-shaped probability weighting lead to larger portfolio allocations.2010 Mathematics Subject Classification. Primary: 91G10; Secondary: 91B06, 91B16.

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Section: 1mentioning

confidence: 94%

mentioning

confidence: 99%

Inverse S-shaped probability weighting and its impact on investment

He¹,

Kouwenberg²

2018

MCRF

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“…The difficulty of non-concavity was overcome by the quantile approach developed in Jin and Zhou (2008), Carlier and Dana (2011), He and Zhou (2011), and Xu (2016). A general solution for a rank-dependent utility maximization problem in a complete market was derived in Xia and Zhou (2016) and its effects on optimal investment decisions were extensively studied in He and Zhou (2016) and He et al (2017). A solution for a sophisticated agent who is not able to pre-commit was recently obtained in Hu et al (2020).…”

Section: Introductionmentioning

confidence: 99%

“…A general solution for a rank‐dependent utility maximization problem in a complete market was derived in Xia and Zhou (2016) and its effects on optimal investment decisions were extensively studied in He and Zhou (2016) and He et al. (2017). A solution for a sophisticated agent who is not able to pre‐commit was recently obtained in Hu et al.…”

Section: Introductionmentioning

confidence: 99%

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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Cost-efficient payoffs under model ambiguity

Bernard,

Junike,

Lux

et al. 2024

Finance Stoch

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Dybvig (1988a, 1988b) solves in a complete market setting the problem of finding a payoff that is cheapest possible in reaching a given target distribution (“cost-efficient payoff”). In the presence of ambiguity, the distribution of a payoff is, however, no longer known with certainty. We study the problem of finding the cheapest possible payoff whose worst-case distribution stochastically dominates a given target distribution (“robust cost-efficient payoff”) and determine solutions under certain conditions. We study the link between “robust cost-efficiency” and the maxmin expected utility setting of Gilboa and Schmeidler (1989), as well as more generally in a possibly nonexpected robust utility setting. Specifically, we show that solutions to maxmin robust expected utility are necessarily robust cost-efficient. We illustrate our study with examples involving uncertainty both on the drift and on the volatility of the risky asset.

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Rank-Dependent Utility and Risk Taking in Complete Markets

Cited by 29 publications

References 42 publications

Inverse S-shaped probability weighting and its impact on investment

Inverse S-shaped probability weighting and its impact on investment

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

Cost-efficient payoffs under model ambiguity

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