Optimal control theory and differential game theory is applied to the study of the defense of high value airborne assets, particularly in the case of a single threat such as an adversarial aircraft or missile. Rather than utilizing onboard defenses of the high value airborne asset, defense is proposed using a teamed unmanned combat air vehicle. The common scenario throughout this dissertation involves the defense of a high value airborne asset (evader) teamed with an unmanned combat vehicle (defender) against a single threat (pursuer). The unmanned combat air vehicle (defender), provides defense in one of two ways: kinetic or directed energy. When defense is kinetic in nature, the defender launches a missile which strives to reach the threat before the threat reaches the high value airborne asset – damage to the pursuer is dealt through capture. When defense is provided through directed energy, the defender strives to keep the incoming threat inside his weapon engagement zone for as long as possible – damage to the pursuer is dealt over time. Leveraging differential game theory and optimal control theory, a series of scenarios are proposed and solved which illustrate different optimal strategies for the successful defense of a high value airborne asset against the incoming threat. In the event that defense is kinetic in nature, the defender-evader team strives to be as far (in range) from the captured pursuer at final time while the pursuer strives to minimize said range. When defense is provided by means of directed energy, the pursuer strives to capture the evader in minimum time while the defender strives to maximally expose the pursuer prior to the evader’s capture. In addition to considering the optimal strategies for the successful defense of a high value airborne asset against an incoming threat, an investigation of various numerical methods is conducted. The investigation compares and contrasts four different direct methods. The comparisons between the different numerical methods are used to suggest a single method that may be applicable for future hardware implementation.