Along the left-lateral strike-slip fault on the eastern border of the Tibetan plateau, 22 M ≥ 6 earthquakes have occurred since 1725. The fault is divided into three segments with two aseismic gaps between the segments. Using the elasticity theory of dislocations, the spatial and temporal variations in stress are calculated using source parameters from the earthquakes such as epicenter, time, length of surface rupture, mean coseismic displacement and magnitude. Further, a total slip rate is assumed in order to calculate the stress increase due to plate motion. The model is optimized towards the smallest variations in the preseismic stresses. Under this constraint, the present stress field is calculated by varying the spatial distribution of the ratio of seismic slip to total slip and the unknown initial stress field. The greatest seismic hazard is found in the central segment, if a spatially constant slip rate is assumed. However, different seismic slip rates for different fault segments lead to the southern segment as the region where the next large earthquake may occur.