A rejuvenating composition for asphalt applications, comprising a polymerized oil comprising a starting material oil crosslinked with elemental sulfur, the polymerized oil comprising a Hildebrand solubility ranging from about 6 to about 12 and a flash point, ranging from about 100° C. to about 400° C. the polymerized oil having a sulfur content of 0.01 wt % to 8.7 wt %, wherein the starting material oil comprises a biorenewable, previously modified, or functionalized oil comprising soybean oil, canola oil, rapeseed oil, castor oil, tall oil, sunflower oil, palm oil, peanut oil, safflower oil, corn oil, corn stillage oil, lecithin, an animal-based oil, or a combination thereof.