In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered.

More from our Archive

• DOI: 10.3390/sym15071324 2023

  The Analysis of Bifurcation, Quasi-Periodic and Solitons Patterns to the New Form of the Generalized q-Deformed Sinh-Gordon Equation

  Syeda Sarwat Kazmi, Adil Jhangeer, Nauman Raza, Haifa I. Alrebdi, Abdel-Haleem Abdel-Aty, Hichem Eleuch

• DOI: 10.3390/math11143069 2023

  An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil

  Raydonal Ospina, João A. M. Gondim, Víctor Leiva, Cecilia Castro

• DOI: 10.1098/rsta.2022.0217 2023

  Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations

  Tobias Dornheim, Jan Vorberger, Zhandos A. Moldabekov, Maximilian Böhme

• DOI: 10.3390/math11143133 2023

  Dynamic RNA Coding Color Image Cipher Based on Chain Feedback Structure

  Heping Wen, Shenghao Kang, Zhuxi Wu, Yiting Lin, Yiming Huang

• DOI: 10.3390/math11143110 2023

  Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures

  Zhifu Jia, Cunlin Li

• DOI: 10.3390/math11143052 2023

  Greenhouse Micro-Climate Prediction Based on Fixed Sensor Placements: A Machine Learning Approach

  Oladayo S. Ajani, Member Joy Usigbe, Esther Aboyeji, Daniel Dooyum Uyeh, Yushin Ha, Tusan Park, Rammohan Mallipeddi

• DOI: 10.3390/math11133022 2023

  Mathematical Modelling of Fused Deposition Modeling (FDM) 3D Printing of Poly Vinyl Alcohol Parts through Statistical Design of Experiments Approach

  Mahmoud Moradi, Mojtaba Karamimoghadam, Saleh Meiabadi, Giuseppe Casalino, Mohammad Ghaleeh, Bobymon Baby, Harikrishna Ganapathi, Jomal Jose, Muhammed Shahzad Abdulla, Paul Tallon, Mahmoud Shamsborhan, Mohammad Rezayat, Satyam Paul, Davood Khodadad

• DOI: 10.3390/math11133008 2023

  Prognostics and Health Management of Rotating Machinery of Industrial Robot with Deep Learning Applications—A Review

  Prashant Kumar, Salman Khalid, Heung Kim

• DOI: 10.3390/sym15071338 2023

  Nonlinear Dynamics of a Piecewise Modified ABC Fractional-Order Leukemia Model with Symmetric Numerical Simulations

  Hasib Khan, Jehad Alzabut, Wafa F. Alfwzan, Haseena Gulzar

• DOI: 10.1002/mma.9474 2023

  Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

  Nabil Chems Eddine, Phuong Duc Nguyen, Maria Alessandra Ragusa