.png){kind=icon}
.png){kind=icon}
Return
Jump-diffusion optimization: An iterative solution to the HJB equation for investment value
.png){kind=icon}
PRE
AI
DOI：10.22034/cmde.2025.68581.3328.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This paper focuses on optimizing the investment value function by incorporating jump risk using the Merton Jump-Diffusion (MJD) model. Our main goal is to determine the optimal dynamic asset allocation strategy to maximize expected utility. We derive the governing nonlinear Hamilton-Jacobi-Bellman (HJB) equation and employ a linearized generalized Newton method, which generates an iterative sequence for the optimal control. The theoretical convergence of this sequence was rigorously established using the Contraction Mapping Theorem, confirming the method's strong stability and reliability. Applying the model to real Go ogle stock data, which exhibit significant jump risks, we derived an optimal investment ratio (pi & lowast;) that suggests a notably aggressive allocation to the risky asset. This optimal strategy provides a direct, actionable benchmark for investors. Crucially, the derived dynamic control law functions as a powerful tool for investment management firms, enabling them to proactively adjust capital allocation strategies in response to potential future jump risk scenarios.
Keywords:
Investment value function
Jump risk
Merton Jump-diffusion model
Hamilton-Jacobi-Bellman equation
Contraction mapping
Frechet derivative
Journal
C
IF:
1.3
Papers:
52
Citations:
0