A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers

Alia, Ishak; Chighoub, Farid; Sohail, Ayesha

doi:10.1016/j.insmatheco.2016.03.009

Cited by 21 publications

(13 citation statements)

References 27 publications

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“…As a result of the popularity of the application of time-consistent MV optimization to investmentreinsurance problems (see for example Alia et al (2016); Li et al (2015c); Liang and Song (2015)),…”

Section: Discussionmentioning

confidence: 99%

“…The time-consistent MV approach has received considerable attention in recent literature; see, for example, Alia et al (2016); Bensoussan et al (2014); Cui et al (2015); Li et al (2015c); Liang and Song (2015); Sun et al (2016); Zhang and Liang (2017), among many other publications. In particular, as evidenced by these publications, this approach has been very popular in institutional settingsespecially in insurance-related applications, where MV-utility insurers are typically concerned with investment-reinsurance or investment-only optimization problems.…”

Section: Introductionmentioning

confidence: 99%

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Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

Staden

Dang

2018

Insurance: Mathematics and Economics

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We investigate the time-consistent mean-variance (MV) portfolio optimization problem, popular in investment-reinsurance and investment-only applications, under a realistic context that involves the simultaneous application of different types of investment constraints and modelling assumptions, for which a closed-form solution is not known to exist. We develop an efficient numerical partial differential equation method for determining the optimal control for this problem. Central to our method is a combination of (i) an impulse control formulation of the MV investment problem, and (ii) a discretized version of the dynamic programming principle enforcing a time-consistency constraint. We impose realistic investment constraints, such as no trading if insolvent, leverage restrictions and different interest rates for borrowing/lending. Our method requires solution of linear partial integro-differential equations between intervention times, which is numerically simple and computationally effective. The proposed method can handle both continuous and discrete rebalancings. We study the substantial effect and economic implications of realistic investment constraints and modelling assumptions on the MV efficient frontier and the resulting investment strategies. This includes (i) a comprehensive comparison study of the pre-commitment and time-consistent optimal strategies, and (ii) an investigation on the significant impact of a wealth-dependent risk aversion parameter on the optimal controls.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

Staden

Dang

2018

Insurance: Mathematics and Economics

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“…Next we prove (80). By the equality (16) in Theorem 3.3, the objective value ofû (·) at time t ∈ [0, T ] is given by J t,X x0 (t) ;û (·) = θ t t,X x0 (t) + G t,X x0 (t) , g t,X x0 (t) = θ t t,X x0 (t) − 1 2 g t,X x0 (t) 2 (81)…”

Section: Equilibrium Solutionmentioning

confidence: 99%

“…Nash equilibriums are therefore adopted as concepts of solutions to the problem; for a detailed introduction see e.g. [37], [16], [17], [8], [43], [19], [1], [2], [42] and references therein.…”

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confidence: 99%

Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach

Alia¹

2020

Mathematical Control &Amp; Related Fields

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In this paper, we investigate a class of time-inconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. We study these problems within the game theoretic framework, and look for open-loop Nash equilibrium controls. Under suitable conditions, we derive a verification theorem for equilibrium controls via a flow of forwardbackward stochastic partial differential equations. To illustrate our results, we discuss a mean-variance problem with a state-dependent trade-off between the mean and the variance.2010 Mathematics Subject Classification. Primary: 91B51, 93E20, 60H30, 93E99, 60H10; Secondary: 93E25.

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“…The TCMV approach has received considerable attention in recent literature; see, for example, Alia et al (2016); Bensoussan et al (2014); Cui et al (2015); Li et al (2015c); Liang and Song (2015); Sun et al (2016); Zhang and Liang (2017), among many other publications. In particular, as evidenced by these publications, this approach has been very popular in institutional settings -especially in insurance-related applications, where MV-utility insurers are typically concerned with investmentreinsurance or investment-only optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods for mean-risk portfolio optimization

Staden¹,

Marais²

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We consider various aspects of the dynamic mean-risk portfolio optimization problem, with specific focus on the numerical methods to solve this problem in the case where the risk measure is either the variance of wealth outcomes or the quadratic variation of the wealth process. In the case where the risk measure is the variance of wealth outcomes, the mean-risk problem is known as the dynamic mean-variance (MV) portfolio optimization problem. Since variance is not separable in the sense of dynamic programming, the MV objective violates Bellman's principle of optimality. As a result, the possibility of the time-inconsistency of the associated MV-optimal investment strategies leads to a number of competing approaches to formulating and solving the dynamic MV problem. We primarily focus on the two main approaches, namely the time-consistent MV (TCMV) and the pre-commitment MV (PCMV) optimization problems. In addition, this investigation also leads us to consider related approaches which are not necessarily MV optimal in some sense, such as the Mean-Quadratic Variation (MQV) portfolio optimization problem.

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A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers

Cited by 21 publications

References 27 publications

Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach

Numerical methods for mean-risk portfolio optimization

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