Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting

Jin, Hanqing; Xia, Jianming

doi:10.1111/mafi.12200

Cited by 15 publications

(12 citation statements)

References 31 publications

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“…Recent advances on RDU equilibria in complete markets are summarized in Xia and Zhou (2016) and Jin et al (2019). Our paper is essentially different from Xia and Zhou (2016) and Jin et al (2019), noting that our market is comonotone to begin with.…”

Section: Introductionmentioning

confidence: 93%

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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Section: Introductionmentioning

confidence: 93%

Competitive equilibria in a comonotone market

Boonen¹,

Liu²,

Wang³

2020

Econ Theory

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“…Apart from at the boundary points {A, B}, this is the subdifferential of the concave function u 4 . Let α be a constant and let ϕ ∈ F satisfy αq(x) ∈ ∂u(ϕ * (x)) (18) for every x. Then ϕ * is a solution to the maximization problem (19) and the minimization problem Thus ϕ * solves the problem (19).…”

Section: Portfolio Optimization With Limited Liability and Utility Comentioning

confidence: 99%

“…We will consider primarily the four papers [19,29,16,15]. Related research is presented in [18,28,27,26,7,20].…”

Section: Introductionmentioning

confidence: 99%

Optimizing S-Shaped Utility and Implications for Risk Management

Armstrong

Brigo

2018

SSRN Journal

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We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product design aimed at utility maximization is not constrained at all by VaR or ES bounds: the maximized utility corresponding to the optimal payoff is the same with or without ES constraints. By contrast we show that, in reasonable markets, risk management constraints based on a second more conventional concave utility function can reduce the maximum S-shaped utility that can be achieved by the investor, even if the constraining utility function is only rather modestly concave. It follows that product designs leading to unbounded S-shaped utilities will lead to unbounded negative expected constraining utilities when measured with such conventional utility functions. To prove these latter results we solve a general problem of optimizing an investor expected utility under risk management constraints where both investor and risk manager have conventional concave utility functions, but the investor has limited liability. We illustrate our results throughout with the example of the Black-Scholes option market. These results are particularly important given the historical role of VaR and that ES was endorsed by the Basel committee in 2012-2013.

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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

Boonen¹,

Ghossoub²

2020

ASTIN Bull.

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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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Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting

Cited by 15 publications

References 31 publications

Competitive equilibria in a comonotone market

Competitive equilibria in a comonotone market

Optimizing S-Shaped Utility and Implications for Risk Management

Bilateral Risk Sharing With Heterogeneous Beliefs and Exposure Constraints

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