A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control

Parpas, Panos; Webster, Mort

doi:10.1016/j.automatica.2013.02.053

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…Meshfree methods such as MLS have been applied to other problems requiring interpolation in high dimensional space such as scattered data modeling, the solution of partial differential equations, medical imaging, and finance [7]. In the context of stochastic optimization, MLS was applied in [23] in an iterative algorithm that solves for the stochastic maximum principle. Here we apply the method in the context of the dynamic programming principle.…”

Section: Backward Passmentioning

confidence: 99%

An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty

2012

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Analyses of global climate policy as a sequential decision under uncertainty have been severely restricted by dimensionality and computational burdens. Therefore, they have limited the number of decision stages, discrete actions, or number and type of uncertainties considered. In particular, other formulations have difficulty modeling endogenous or decision-dependent uncertainties, in which the shock at time t + 1 depends on the decision made at time t. In this paper, we present a stochastic dynamic programming formulation of the Dynamic Integrated Model of Climate and the Economy (DICE), and the application of approximate dynamic programming techniques to numerically solve for the optimal policy under uncertain and decision-dependent technological change. We compare numerical results using two alternative value function approximation approaches, one parametric and one non-parametric. Using the framework of dynamic programming, we show that an additional benefit to near-term emissions reductions comes from a probabilistic lowering of the

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Section: Backward Passmentioning

confidence: 99%

An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty

2012

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“…In order to apply our value of life analysis, we exploit recent advances in the systems and control literature. Parpas and Webster (2013) show that one can reformulate a stochastic finite-horizon optimization problem as a deterministic problem that takes ( , ( ), ), ≠ , as exogenous. More precisely, we focus on the path of that begins in state and remains in state until time .…”

Section: Iiia the Uninsured Value Of Lifementioning

confidence: 99%

“…We now introduce a one-time opportunity to purchase a flat lifetime annuity, and also endow the consumer with state-dependent life-cycle income, ( ). Recall that we previously solved the consumer's problem for each state by focusing on the path of that begins in state and remains in state until time (Parpas and Webster 2013). Incomplete annuity markets and life-cycle income complicate our analysis by introducing the possibility of multiple sets of non-interior solutions within and across different states.…”

Section: Iiic the Incompletely Annuitized Value Of Lifementioning

confidence: 99%

Mortality Risk, Insurance, and the Value of Life

Bauer¹,

Lakdawalla²,

Reif³

2018

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We develop a new framework for valuing health and longevity improvements that departs from conventional but unrealistic assumptions of full annuitization and deterministic health. Our framework can value the prevention of mortality and of illness, and it can quantify the effects of retirement policies on the value of life. We apply the framework to life-cycle data and generate new insights absent from the conventional approach. First, treatment is up to five times more valuable than prevention, even when both extend life equally. This asymmetry helps explain low observed investment in preventive care. Second, severe illness can significantly increase the value of statistical life, helping to reconcile theory with empirical findings that consumers value life-extension more in bleaker health states. Third, retirement annuities boost aggregate demand for life-extension. We calculate that Social Security adds $10.6 trillion (11 percent) to the value of post-1940 longevity gains and would add $127 billion to the value of a one percent decline in future mortality.

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Multiobjective control for nonlinear stochastic Poisson jump-diffusion systems via T-S fuzzy interpolation and Pareto optimal scheme

Chen

Zhang

2020

Fuzzy Sets and Systems

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A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control

Cited by 6 publications

References 19 publications

An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty

An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty

Mortality Risk, Insurance, and the Value of Life

Multiobjective control for nonlinear stochastic Poisson jump-diffusion systems via T-S fuzzy interpolation and Pareto optimal scheme

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