Stress is widely recognized as a major contributor to a variety of health issues. Stress prediction using biosignal data recorded by wearables is a key area of study in mobile sensing research because real-time stress prediction can enable digital interventions to immediately react at the onset of stress, helping to avoid many psychological and physiological symptoms such as heart rhythm irregularities. Electrodermal activity (EDA) is often used to measure stress. However, major challenges with the prediction of stress using machine learning include the subjectivity and sparseness of the labels, a large feature space, relatively few labels, and a complex nonlinear and subjective relationship between the features and outcomes. To tackle these issues, we examine the use of model personalization: training a separate stress prediction model for each user. To allow the neural network to learn the temporal dynamics of each individual's baseline biosignal patterns, thus enabling personalization with very few labels, we pre-train a 1-dimensional convolutional neural network (CNN) using self-supervised learning (SSL). We evaluate our method using the Wearable Stress and Affect prediction (WESAD) dataset. We fine-tune the pre-trained networks to the stress prediction task and compare against equivalent models without any self-supervised pre-training. We discover that embeddings learned using our pre-training method outperform supervised baselines with significantly fewer labeled data points: the models trained with SSL require less than 30% of the labels to reach equivalent performance without personalized SSL. This personalized learning method can enable precision health systems which are tailored to each subject and require few annotations by the end user, thus allowing for the mobile sensing of increasingly complex, heterogeneous, and subjective outcomes such as stress.