Robust time-inconsistent stochastic control problems

Pun, Chi Seng

doi:10.1016/j.automatica.2018.04.038

Cited by 40 publications

(26 citation statements)

References 30 publications

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“…2) We incorporate the stochastic labor income factor into our model and link it to the contribution premiums, which leads to a more complicated problem than that in Pun [37]. Moreover, our choice of the ambiguity preference functions extends the specifications of the ambiguity preference function in Maenhout [30] and Pun [37]. 3) We provide rigorous mathematical definition for the robust equilibrium control-measure policy which extends and improves the definition in Zeng et al [51].…”

Section: (Communicated By Phillip Yam)mentioning

confidence: 94%

“…Zeng et al [51] extend the analysis to a reinsurance-investment problem for an AAI who faces uncertainties regarding models in the financial and insurance markets with jumps. Pun [37] establishes a general tractable framework for robust time-inconsistent stochastic control problems. Zeng et al [52] provide a derivative-based optimal policy for an ambiguity-averse pension investor who faces not only risks from stochastic income and market return volatility but also uncertain economic conditions.…”

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

“…Moreover, we define alternative models which are equivalent to the reference model in terms of probability measure. In addition, inspired by Pun [37], we propose two ambiguity preference functions which are economically meaningful and facilitate analytical tractability. We adopt a minmax formulation to construct the robust decision rule.…”

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

“…This problem is still an open question. 2) We incorporate the stochastic labor income factor into our model and link it to the contribution premiums, which leads to a more complicated problem than that in Pun [37]. Moreover, our choice of the ambiguity preference functions extends the specifications of the ambiguity preference function in Maenhout [30] and Pun [37].…”

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

“…We can see that the dissimilarity between the alternative model Q and the reference model P is characterized by q(t). In other words, choosing the measure Q is equivalent to determining the pair of stochastic processes q(t) for a given P. Noting that the measure Q is fully characterized by {q(t)} t∈[0,T ] and the reference model, we denote by (u, q) = {u(t, x, l)} t∈[0,T ] , {q(t, x, l, u)} t∈[0,T ] the control-measure policy, which is also adopted by Pun [37]. Let U × Q be the set of admissible control-measure policies (the definition of the admissible control-measure policy will be given below).…”

Section: 2mentioning

confidence: 99%

See 4 more Smart Citations

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Wang¹,

Chen²,

Yang³

2021

Journal of Industrial &Amp; Management Optimization

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Section: (Communicated By Phillip Yam)mentioning

confidence: 94%

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

Section: (Communicated By Phillip Yam)mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

See 3 more Smart Citations

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Wang¹,

Chen²,

Yang³

2021

Journal of Industrial &Amp; Management Optimization

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Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Yoshioka

2019

Optim Control Appl Methods

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An optimization problem of controlling a dam installed in a river is analyzed based on a stochastic control formalism of a diffusion process under model ambiguity: a new mathematical approach to this issue. The diffusion process is a pathwise unique solution to a water balance equation considering the inflow, outflow, water loss in the reservoir, and direct rainfall. Finding the optimal reservoir operation policy reduces to solving a degenerate parabolic partial differential equation: a Hamilton-Jacobi-Bellman-Isaacs equation. A monotone finite difference scheme is constructed for discretization of the equation, successfully generating nonoscillatory and reasonably accurate numerical solutions. Stability analysis of the resulting water balance dynamics is finally carried out for both environmentally friendly and not friendly reservoir operations. KEYWORDS finite difference scheme, Hamilton-Jacobi-Bellman-Isaacs equation, reservoir operation, stochastic control, viscosity solution INTRODUCTIONThis paper contributes to providing a mathematical framework for modeling and control of reservoirs created in rivers.Since the problem has an engineering background, it is first presented, and then, the issues to be addressed and our contributions are explained.Many rivers have dams serving as central infrastructures to supply essential water resources for human lives. 1-3 The stored water in the reservoir created by a dam is utilized for multiple purposes, such as drinking water, irrigation, and hydropower generation. 4 Several dams are used for flood mitigation as well. 5,6 On the other hand, controlling a dam critically affects its downstream river environment because the original flow regime is altered. 7-9 Sediment transport and attached algae population dynamics in dam downstream experience significant changes because dams trap sediment and the algae growth is highly flow-dependent. 10 Dam operation is thus desired to be environmentally friendly such that its impacts on the downstream are minimized, while it should be fit-for-purpose at the same time.Management of environment and ecology in rivers has been a long-standing engineering problem, 11-13 and mathematical tools and concepts for their modeling, analysis, and control are still developing. Several researchers considered river management problems based on stochastic process models such as stochastic differential equations (SDEs) 14 that can naturally consider stochasticity involved in environmental and ecological processes. 15 Interactions between aquatic species, such as riparian vegetation and fishes, and river discharges have been described with SDEs. 16 Miyamoto and Kimura 17 analyzed seedling, growth, and mortality dynamics of riparian trees subject to stochastic flood disturbances. Vesipa et al 18 764

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Robust classical-impulse stochastic control problems in an infinite horizon

Pun

2022

Math Meth Oper Res

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Robust time-inconsistent stochastic control problems

Cited by 40 publications

References 30 publications

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Robust classical-impulse stochastic control problems in an infinite horizon

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