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Discrete-time risk-aware optimal switching with non-adapted costs

Part of: Stochastic systems and control Stochastic processes Mathematical economics Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  06 June 2022

Randall Martyr Open the ORCID record for Randall Martyr [Opens in a new window] ,
John Moriarty Open the ORCID record for John Moriarty [Opens in a new window]  and
Magnus Perninge
Randall Martyr*
Affiliation:
Kingston University London
John Moriarty*
Affiliation:
Queen Mary University of London
Magnus Perninge*
Affiliation:
Linnaeus University
*
*Postal address: River House, 5357 High Street, Surrey, UK. Email address: [email protected]
**Postal address: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, UK. Email address: [email protected]
***Postal address: PG Vejdes väg 7, 352 52 Växjö, Sweden.
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Abstract

We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision-maker is risk-aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example application to hydropower planning is provided.

Keywords

Infinite horizonoptimal switchingrisk measuresreflected backward stochastic difference equationshydropower planning

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 91B08: Individual preferences 49N30: Problems with incomplete information
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 2 , June 2022 , pp. 625 - 655
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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