Bottom line: Indications for anticoagulants for primary prevention of left ventricular thrombosis include patients with the following traits: large anterior infarctions (particularly in the anterior location), heart failure, and high embolic risk (including those with echocardiographic evidence of mobile and protruding thrombi, severe left ventricular dysfunction, or prior emboli).
Sources (two review articles):
Antithrombotic therapy in left ventricular thrombosis and systemic embolism. L L Cregler. The American heart journal, 1992, Vol.123(4 Pt 2), p.1110-1114.
Antithrombotic therapy in acute myocardial infarction: prevention of venous, left ventricular and coronary artery thromboembolism. B Stein, V Fuster. The American journal of cardiology, 1989, Vol.64(4), p.33B-40B.