A Digital Model for Managing Financial Risks of Investment Operations

Abstract

This paper presents a novel continuous linear-quadratic optimal control framework designed to enhance asset
allocation and mitigate systemic financial risks within highly volatile capital markets. By utilizing a dynamic decision-making
architecture, the proposed digital model effectively streamlines portfolio management cycles without relying on
computationally expensive iterative linear transformations. The underlying mathematical structure incorporates positive
definite risk-weighted matrices focused on both transaction cost reduction and terminal risk minimization based on Bellman
optimality principles. Furthermore, the local and semi-local convergence parameters of the associated Riccati differential
sequences are rigorously established under classical Lipschitz conditions to guarantee stability. Extensive numerical simulations
demonstrate that the model exhibits exceptional robustness and mathematical resilience during periods of intense market
fluctuations, making it a highly reliable tool for modern corporate financial engineering and algorithmic trading systems.