Optimal Portfolio Selection With VaR and Portfolio Insurance Constraints Under Rank-Dependent Expected Utility Theory

Mi, Hui; Xu, Zuo Quan

doi:10.2139/ssrn.3880289

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…when w is inverse S-shaped) can be solved by the quantile optimization method developed recently. We refer interested readers to [10,20,11,17,19,21] for details.…”

Section: A Class Of Law-invariant Driversmentioning

confidence: 99%

<i>g</i>-expectation of distributions

Xu¹,

Xu²

2022

PUQR

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We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant g-expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.

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“…when w is inverse S-shaped) can be solved by the quantile optimization method developed recently. We refer interested readers to [10,20,11,17,19,21] for details.…”

Section: A Class Of Law-invariant Driversmentioning

confidence: 99%

<i>g</i>-expectation of distributions

Xu¹,

Xu²

2022

PUQR

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“…Generally speaking, the probability measure µ in (2.3) makes the preference E a nonlinear expectation (in fact, it is a Choquet expectation), so the problem (2.4) is a challenging non-concave optimization problem. To tackle the problem (2.4), we use the so-called quantile optimization method; see [5,6,3,18,14,33,2,31,16,29,28,34,32,24] for the recent development of this method.…”

Section: Assumption 21 the Quantile Functionmentioning

confidence: 99%

Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory

2022

Scandinavian Actuarial Journal

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This paper investigates a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk neutral and employs the mean-variance premium principle. To eliminate potential moral hazard issues, we only consider the so-called moral-hazard-free insurance contracts that obey the incentive compatibility constraint. The insurance problem is first formulated as a non-concave maximization problem involving Choquet expectation, then turned into a concave quantile optimization problem and finally solved by the calculus of variations method. The optimal contract is expressed by a second-order ordinary integro-differential equation with nonlocal operator. An effective numerical method is proposed to compute the optimal contract assuming the probability weighting function has a density. Also, we provide an example which is analytically solved.

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“…This approach, coined as the "quantile formulation" by [10], was taken in Jin and Zhou [9] to solve for the first time a behavioral portfolio selection problem with probability distortion and S-shaped utility functions. It is subsequently employed to solve various non-expected utility portfolio selection problems, such as in [10,18,17,19,12].…”

Section: Introductionmentioning

confidence: 99%

$g$-Expectation of Distributions

Xu¹,

Xu²

2022

Preprint

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Optimal Portfolio Selection With VaR and Portfolio Insurance Constraints Under Rank-Dependent Expected Utility Theory

Cited by 3 publications

References 26 publications

<i>g</i>-expectation of distributions

<i>g</i>-expectation of distributions

Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory

$g$-Expectation of Distributions

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