Control with partial observations and an explicit solution of Mortensen's equation

Václav E. Benes; Ioannis Karatzas; Daniel Ocone; Hui Wang

doi:10.1007/s00245-003-0788-0

Control with partial observations and an explicit solution of Mortensen's equation

Václav E. Benes, Ioannis Karatzas, Daniel Ocone, Hui Wang

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.

Original language	English (US)
Pages (from-to)	217-239
Number of pages	23
Journal	Applied Mathematics and Optimization
Volume	49
Issue number	3
DOIs	https://doi.org/10.1007/s00245-003-0788-0
State	Published - May 2004

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

Keywords

Filtering
Komlós theorem
Mortensen equation
Partial observations
Recursive stochastic equations
Stochastic control

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10.1007/s00245-003-0788-0

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abstract = "We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the {"}signal-plus-noise{"} type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.",

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T1 - Control with partial observations and an explicit solution of Mortensen's equation

AU - Benes, Václav E.

AU - Karatzas, Ioannis

AU - Ocone, Daniel

AU - Wang, Hui

PY - 2004/5

Y1 - 2004/5

N2 - We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.

AB - We formulate a stochastic control problem with a general information structure, and show that an optimal law exists and is characterized as the unique solution of a recursive stochastic equation. For a special information structure of the "signal-plus-noise" type and with quadratic cost-functions, this recursive equation is solved for the value function of the control problem. This value function is then shown to satisfy the Mortensen equation of Dynamic Programming in function-space.

KW - Filtering

KW - Komlós theorem

KW - Mortensen equation

KW - Partial observations

KW - Recursive stochastic equations

KW - Stochastic control

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JO - Applied Mathematics and Optimization

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ER -

Control with partial observations and an explicit solution of Mortensen's equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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