Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively and to avoid obstacles in a forward-looking way. The task of collision avoidance can be divided into a global and a local level. Regarding the global level, we propose an approach called "Predictive Collision Management Path Planning" (PCMP). At the local level, solutions for collision avoidance are used that prevent an inevitable collision. Therefore, the aim of PCMP is to avoid unnecessary local collision scenarios using predictive collision management. PCMP is a graph-based algorithm with a focus on the time dimension consisting of three parts: (1) movement prediction, (2) integration of movement prediction into a time-dependent graph, and (3) time and risk-dependent path planning. The algorithm combines the search for a shortest path with the question: is the detour worth avoiding a possible collision scenario? We evaluate the evasion behavior in different simulation scenarios and the results show that a risk-sensitive agent can avoid 47.3% of the collision scenarios while making a detour of 1.3%. A risk-averse agent avoids up to 97.3% of the collision scenarios with a detour of 39.1%. Thus, an agent's evasive behavior can be controlled actively and risk-dependent using PCMP.