Hierarchical approaches in modeling and numerical simulation for mathematical finance / Anna Lisa Clevenhaus. Wuppertal, 2025-09-25
Inhalt
- Acknowledgement
- Foreword
- List of Symbols
- List of Figures
- List of Tables
- List of Algorithms
- Introduction
- Temporal Discretization
- Spatial Discretization
- Spatial Grids
- Finite Difference Methods
- Sparse Grids
- Combination of the Sparse Grids and the Parareal
- Financial models
- Adjustment for Financial Models
- The Black-Scholes Model
- The Heston Model
- Transformations of the Heston Model
- Space Mapping
- Numerical Results
- The Penalty Term for the Black-Scholes Model
- Sparse Grids for the Heston Model
- Parareal and the Combination with the Sparse Grids for the Heston Model
- Boundary Conditions for the Heston Model
- Gradient Descent Algorithm for the Heston Model
- Space Mapping for the Heston Model
- Conclusion and Outlook