Adjustable cash inflows based online investment decision making

• Adjustable cash inflows are first introduced into online investment decision making • The farsighted strategy is designed by focusing on returns in the next two periods. • The trust region method is proposed to solve the complicated nonlinear programming. • The advantages of ACIE and ACIE2 are validated adequately in practical experiments. Online portfolio selection tackles the sequential investment decision making and optimization issues with the market information updated constantly. In this work, we propose two novel online portfolio selection algorithms , ACIE and ACIE2, for online investment with dynamically adjustable cash inflows. Unlike traditional models that assume a fixed capital base , our framework allows investors to flexibly adjust capital injection levels over time, guided by return forecasting. ACIE optimizes portfolio weights and cash inflow proportion in a single-period setting, while ACIE2 extends this to a two-period lookahead optimization, offering improved stability and foresight. Both models are formulated as nonlinear constrained optimization problems, which can be solved by trust region interior point methods. Extensive experiments across four real-world datasets validate that our methods outperform a broad range of baseline strategies in terms of cumulative wealth , Sharpe ratio, and Calmar ratio. Additionally, we demonstrate that the dynamic cash inflow mechanism enhances risk control and adapts effectively to different market environments , making our approach practical and effective for real-world investment management.