Risk-sensitive mean-field-type control

Alain Bensoussan; Boualem Djehiche; Hamidou Tembine; Phillip Yam

doi:10.1109/CDC.2017.8263639

Risk-sensitive mean-field-type control

Alain Bensoussan
, Boualem Djehiche
, Hamidou Tembine^*
, Phillip Yam

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

5 Citations (Scopus)

Abstract

We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Publisher	IEEE
Pages	33-38
ISBN (Electronic)	9781509028733
ISBN (Print)	9781509028740
DOIs	https://doi.org/10.1109/CDC.2017.8263639
Publication status	Published - Dec 2017
Event	56th IEEE Conference on Decision and Control (CDC 2017) - Melbourne Convention Center, Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017 Conference number: 56 http://cdc2017.ieeecss.org/

Conference

Conference	56th IEEE Conference on Decision and Control (CDC 2017)
Abbreviated title	CDC 2017
Place	Australia
City	Melbourne
Period	12/12/17 → 15/12/17
Internet address	http://cdc2017.ieeecss.org/

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abstract = "We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.",

author = "Alain Bensoussan and Boualem Djehiche and Hamidou Tembine and Phillip Yam",

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AU - Bensoussan, Alain

AU - Djehiche, Boualem

AU - Tembine, Hamidou

AU - Yam, Phillip

N1 - Conference code: 56

PY - 2017/12

Y1 - 2017/12

N2 - We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.

AB - We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.

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UR - https://www.scopus.com/pages/publications/85046143547#tab=impact

U2 - 10.1109/CDC.2017.8263639

DO - 10.1109/CDC.2017.8263639

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9781509028740

SP - 33

EP - 38

BT - 2017 IEEE 56th Annual Conference on Decision and Control (CDC)

PB - IEEE

T2 - 56th IEEE Conference on Decision and Control (CDC 2017)

Y2 - 12 December 2017 through 15 December 2017

ER -

Risk-sensitive mean-field-type control

Abstract

Conference

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