Switching problems with controlled randomisation and associated obliquely reflected BSDEs

被引：6

作者：

Benezet, Cyril ^{[1
]}

Chassagneux, Jean-Francois ^{[2
,3
]}

Richou, Adrien ^{[4
,5
]}

机构：

[1] Univ Paris Saclay, Univ Evry, Lab Math & Modelisat Evry, ENSIIE,CNRS, F-91037 Evry, France

[2] Univ Paris, UFR Math, Batiment Sophie Germain,8 Pl Aurelie Nemours, F-75013 Paris, France

[3] Univ Paris, LPSM, Batiment Sophie Germain,8 Pl Aurelie Nemours, F-75013 Paris, France

[4] Univ Bordeaux, UMR 5251, F-33400 Talence, France

[5] Univ Bordeaux, IMB, F-33400 Talence, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2022年 / 144卷

关键词：

Optimal switching with uncertainty; Backward stochastic differential equations; Oblique reflections; Enlargement of filtrations; STOCHASTIC DIFFERENTIAL-EQUATIONS; BACKWARD;

D O I：

10.1016/j.spa.2021.10.010

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value of the switching problem is related to a new class of multidimensional obliquely reflected BSDEs. These BSDEs allow as well to construct an optimal strategy and thus to solve completely the initial problem. The other main contribution of our work is to prove new existence and uniqueness results for these obliquely reflected BSDEs. This is achieved by a careful study of the domain of reflection and the construction of an appropriate oblique reflection operator in order to invoke results from Jean-Francois Chassagneux and Adrien Richou (2020). (C) 2021 Elsevier B.V. All rights reserved.

引用

页码：23 / 71

页数：49

共 37 条

[1] OPTIMAL SWITCHING OF ONE-DIMENSIONAL REFLECTED BSDES AND ASSOCIATED MULTIDIMENSIONAL BSDES WITH OBLIQUE REFLECTION
Tang, Shanjian
Zhong, Wei
Koo, Hyeng Keun
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (06) : 2279 - 2317
[2] Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems
Chassagneux, Jean-Francois
Richou, Adrien
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (11) : 4597 - 4637
[3] Quadratic reflected BSDEs and related obstacle problems for PDEs
Huang, Zongyuan
Wang, Haiyang
Wu, Zhen
Yu, Zhiyong
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2020, 49 (03) : 567 - 589
[4] Reflected BSDEs with logarithmic growth and applications in mixed stochastic control problems
El Asri, Brahim
Oufdil, Khalid
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2023, 95 (01) : 23 - 53
[5] SWITCHING GAME OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND ASSOCIATED SYSTEM OF OBLIQUELY REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Hu, Ying
Tang, Shanjian
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (11) : 5447 - 5465
[6] Systems of BSDES with oblique reflection and related optimal switching problems
Topolewski, Mateusz
[J]. STOCHASTICS AND DYNAMICS, 2019, 19 (04)
[7] Optimal switching, systems of reflected BSDEs and systems of variational inequalities with inter-connected obstacles
Hamadene, Said
[J]. SURVEYS IN STOCHASTIC PROCESSES, 2011, : 1 - 27
[8] Reflected BSDEs with random default time and related mixed optimal stopping-control problems
Dong-mei Guo
Xiao-ming Xu
[J]. Acta Mathematicae Applicatae Sinica, English Series, 2013, 29 : 165 - 178
[9] Reflected BSDEs with random default time and related mixed optimal stopping-control problems
Guo, Dong-mei
Xu, Xiao-ming
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2013, 29 (01): : 165 - 178
[10] Reflected BSDEs with Random Default Time and Related Mixed Optimal Stopping-control Problems
Dong-mei Guo
Xiao-ming Xu
[J]. Acta Mathematicae Applicatae Sinica, 2013, (01) : 165 - 178

← 1 2 3 4 →