Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects
| Autor: | Dan GOREAC, Juan LI, Boxiang XU |
|---|---|
| Přispěvatelé: | School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, PR China, Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Research Center for Mathematics and Interdisciplinary Sciences, Shandong University,Qingdao 266237, P. R. China |
| Rok vydání: | 2022 |
| Předmět: |
49M29
dual algorithm. MSC2020 Classification. 65K10 Applied Mathematics Probability (math.PR) 65K15 Mathematics::Optimization and Control linear programming 93E20 91G50 [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Computational Mathematics dual dynamic programming Optimization and Control (math.OC) FOS: Mathematics occupation measure 65C30 [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 49M20 93-08 Singular/continuous control Mathematics - Optimization and Control 49J40 Mathematics - Probability |
| Zdroj: | Applied Mathematics and Computation Applied Mathematics and Computation, Elsevier, 2022, 431, pp.127321. ⟨10.1016/j.amc.2022.127321⟩ |
| ISSN: | 0096-3003 |
| DOI: | 10.48550/arxiv.2206.10224 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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