The rapid growth in automated financial trading has highlighted the need for trustworthy agents capable of adapting to the dynamic and ever-changing nature of financial markets. From an algorithmic viewpoint, financial trading is essentially a complex, dynamic time series problem, characterized by unpredictable and noisy data. Deep Reinforcement Learning (DRL) has shown great promise in addressing this challenge. It naturally aligns with the objective of financial trading-maximizing rewards-without relying on unrealistic assumptions that do not hold true in such volatile and noisy time series data. However, the complexity of the problem still presents challenges for conventional DRL algorithms. To overcome these, the implementation of continual learning agents is crucial for their ability to adjust to changing market conditions. Our approach not only adapts continual learning techniques to dynamic time series but also introduces a novel knowledge transfer loss, which enhances the adaptation of our model. In our extensive evaluation, we show that this approach successfully balances the trade-off between maintaining knowledge of past patterns and adapting to new ones, enhancing the model’s trustworthiness and effectiveness in real-world time series problems, like financial trading.