Arrow–debreu Equilibria for Rank‐dependent Utilities

Xia, Jianming; Zhou, Xun Yu

doi:10.1111/mafi.12070

Cited by 72 publications

(59 citation statements)

References 34 publications

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“…Proof of Theorem 2 This is a direct consequence of Theorem 3.3 in Xia and Zhou (2013). Note that we do not have consumption at time 0.…”

Section: Appendix B Proofsmentioning

confidence: 80%

“…In the following, we need to use Lemma B.6 in Xia and Zhou (2013). For readers' convenience, we reproduce this lemma here (with change of notations):…”

Section: Appendix a Some Results On Convex Envelopesmentioning

confidence: 99%

“…Problem (2) has recently been studied extensively; see Carlier and Dana (2011), He and Zhou (2014), and Xia and Zhou (2013). Here, we cite a general result provided in Xia and Zhou (2013). To this end, we recall the definition of the concave and the convex envelopes of a function:…”

Section: Portfolio Selection Modelmentioning

confidence: 99%

“…In addition, the function N(•), defined as in Eq. (3.10) in Xia and Zhou (2013), is the same as in (4).…”

Section: Appendix B Proofsmentioning

confidence: 99%

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Rank-Dependent Utility and Risk Taking in Complete Markets

He¹,

Kouwenberg²

2017

SIAM J. Finan. Math.

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We analyze the portfolio choice problem of investors who maximize rankdependent utility in a single-period complete market. We propose a new notion of less risk taking: choosing optimal terminal wealth that pays off more in bad states and less in good states of the economy. We prove that investors with a less risk averse preference relation in general choose more risky terminal wealth, receiving a risk premium in return for accepting conditional-zero-mean

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“…Proof of Theorem 2 This is a direct consequence of Theorem 3.3 in Xia and Zhou (2013). Note that we do not have consumption at time 0.…”

Section: Appendix B Proofsmentioning

confidence: 80%

“…In the following, we need to use Lemma B.6 in Xia and Zhou (2013). For readers' convenience, we reproduce this lemma here (with change of notations):…”

Section: Appendix a Some Results On Convex Envelopesmentioning

confidence: 99%

Section: Portfolio Selection Modelmentioning

confidence: 99%

“…In addition, the function N(•), defined as in Eq. (3.10) in Xia and Zhou (2013), is the same as in (4).…”

Section: Appendix B Proofsmentioning

confidence: 99%

See 2 more Smart Citations

Rank-Dependent Utility and Risk Taking in Complete Markets

He¹,

Kouwenberg²

2017

SIAM J. Finan. Math.

Self Cite

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“…For instance, Borch (1962), Wilson (1968), Gerber (1978), Bühlmann and Jewell (1979), Kaluszka (2004), and Aase (1993Aase ( , 2010) study the EU case, while Jouini et al (2008) and Ludkovski and Young (2009) study dual utilities (as in Yaari, 1987), or more generally, law-invariant monetary utility functions. Moreover, Tsanakas and Christofides (2006), Xia and Zhou (2016), Jin et al (2019), and Boonen et al (2018) study the case of RDU. As an exception, Boonen (2017) studies Pareto-optimal risk sharing with both expected and dual utilities.…”

Section: Introductionmentioning

confidence: 99%

Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints

Boonen

Ghossoub

2019

SSRN Journal

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This paper studies bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility preferences and the other agent has Rankdependent utility preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing contracts can be obtained via a constrained utility maximization under a participation constraint of the other agent. This allows us to give an explicit characterization of optimal risk-sharing contracts. In particular, we show that an optimal risk-sharing contract contains allocations that are monotone functions of the likelihood ratio, where the latter is obtained from Lebesgue's Decomposition Theorem.

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Competitive equilibria in a comonotone market

Boonen¹,

Liu²,

Wang³

2020

Econ Theory

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We investigate competitive equilibria in a special type of incomplete markets, referred to as a comonotone market, where agents can only trade such that their risk allocation is comonotonic. The comonotone market is motivated by the no-sabotage condition. For instance, in a standard insurance market, the allocation of risk among the insured, the insurer and the reinsurers is assumed to be comonotonic a priori to the risk-exchange. Two popular classes of preferences in risk management and behavioral economics, dual utilities (DU) and rank-dependent expected utilities (RDU), are used to formulate agents’ objectives. We present various results on properties and characterization of competitive equilibria in this framework, and in particular their relation to complete markets. For DU-comonotone markets, we find the equilibrium in closed form and for RDU-comonotone markets, we find the equilibrium in closed form in special cases. The fundamental theorems of welfare economics are established in both the DU and RDU markets. We further propose an algorithm to numerically obtain competitive equilibria based on discretization, which works for both the DU-comonotone market and the RDU-comonotone market. Although the comonotone and complete markets are closely related, many of our findings are intriguing and in sharp contrast to results in the literature on complete markets in terms of existence, uniqueness, and closed-form solutions of the equilibria, and comonotonicity of the pricing kernel.

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Arrow–debreu Equilibria for Rank‐dependent Utilities

Cited by 72 publications

References 34 publications

Rank-Dependent Utility and Risk Taking in Complete Markets

Rank-Dependent Utility and Risk Taking in Complete Markets

Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints

Competitive equilibria in a comonotone market

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