Behavioral and Psychological Symptoms of Dementia (BPSD) impact dementia care substantially, affecting both patients and caregivers. Effective management and early detection of BPSD are crucial to reduce the stress and burden on caregivers and healthcare systems. Despite the advancements in machine learning for dementia prediction, there is a considerable gap in utilizing these methods for BPSD prediction. This study aims to fill this gap by presenting a novel personalized framework for BPSD prediction, utilizing physiological signals from smart wearable devices. Our personalized fine-grained BPSD prediction method accurately predicts BPSD occurrences by extracting individual behavioral patterns, while the generalized models identify diverse patterns and differentiate between various BPSD symptoms. Detailed comparisons between the proposed personalized method and conventional generalized methods reveals substantial improvements across all performance metrics, including a 16.0% increase in AUC. These results demonstrate the potential of our proposed method in advancing dementia care by enabling proactive interventions and improving patient outcomes in real-world scenarios. To the best of our knowledge, this is the first study that leverages physiological signals from smart wearable devices to predict BPSD, marking a significant stride in dementia care research.