Robust Time-Inconsistent Stochastic Control Problems

Pun, Chi Seng

doi:10.2139/ssrn.3035656

Cited by 7 publications

(34 citation statements)

References 31 publications

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“…Proof. This theorem can be proved in a similar way as that in Theorem 5.2 of Björk et al [6] and Theorem 5 of Pun [38], thus we omit it.…”

Section: Theorem 34 (Verification Theorem)mentioning

confidence: 88%

“…Following the derivations in Björk et al [6] and Pun [38], using the EDPE (17), Definition 3.1 and the infinitesimal operator, we can obtain the following extended HJBI system of equations and verification theorem.…”

Section: 2mentioning

confidence: 99%

“…where a(t) and b(t) are given in (38). Substituting (60)-(61) into (28)-(29), we have q * 1 (t, x, l, u * ) = ξ m(t, x, l) n(t, x, l) ,…”

Section: Proof Of Theorem 36mentioning

confidence: 99%

See 2 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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“…Proof. This theorem can be proved in a similar way as that in Theorem 5.2 of Björk et al [6] and Theorem 5 of Pun [38], thus we omit it.…”

Section: Theorem 34 (Verification Theorem)mentioning

confidence: 88%

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

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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“…Based on , the SDE becomes

normald V_{t} = normalΔ Q (() V_{t}, Q_{t}, q_{t}) ((), ((), 1 + σ ((), V_{t}) h_{t}) normald t + σ ((), V_{t}) normald B_{t}),

which is an SDE having an additional drift Δ Q ( V t , Q t , q t ) σ ( V t ) h t . As discussed by Pun, h t is a control variate by “nature” from the viewpoint of differential game theory. The optimization problem presented later is a dynamic game played by the decision‐maker against nature who can alter the probability space through controlling h t .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Instead, the following assumption is hereafter employed for the sake of simplicity of analysis since our focus is not only on mathematical analysis but also on model application. This kind of assumption seems to be restrictive, but is a widely acceptable one in stochastic control problems (see definition 1(3) in the work of Pun and definition 2.1(3) in the work of Zawisza).…”

Section: Mathematical Analysismentioning

confidence: 99%

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 state-dependent mean–variance portfolio selection: a closed-loop approach

2021

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This paper studies a class of robust mean-variance portfolio selection problems with state-dependent risk aversion. Model uncertainty, in the sense of considering alternative dominated models, is introduced to the problem to reflect the investor's uncertainty-averse preference. To characterise the robust portfolios, we consider closed-loop equilibrium control and spike variation approaches. Moreover, we show that the closed-loop equilibrium strategy exists and is unique under some technical conditions. That partially addresses the open problem left in Björk et al. (2017, Finance Stoch.) and Pun (2018, Automatica). By using the necessary and sufficient condition for the equilibrium, we manage to derive the analytical form of the equilibrium strategy via the unique solution to a nonlinear ordinary differential equation system. To validate the proposed closed-loop control framework, we show that when there is no uncertainty, our equilibrium strategy is reduced to the strategy in Björk et al. (2014, Math. Finance), which cannot be deduced under the open-loop control framework.

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Robust Time-Inconsistent Stochastic Control Problems

Cited by 7 publications

References 31 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 state-dependent mean–variance portfolio selection: a closed-loop approach

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