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Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects

Abstract : This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cramér-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation translates into a dual dynamic programming (DDP) algorithm. An important part of the paper is dedicated to structural considerations allowing reasonable implementation. We also hint connections to methods relying on moment sum of squares and LMI (linear matrix inequality)-relaxations to approximate the optimal candidates.
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https://hal.archives-ouvertes.fr/hal-03698524
Contributor : Dan Goreac Connect in order to contact the contributor
Submitted on : Saturday, June 18, 2022 - 10:02:30 AM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM

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Dan Goreac, Juan Li, Boxiang Xu. Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects. Applied Mathematics and Computation, Elsevier, 2022, 431, pp.127321. ⟨10.1016/j.amc.2022.127321⟩. ⟨hal-03698524⟩

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