The key to this question is recognising that varices bleed because of elevated pressure in the portal venous system, so the pharmacological aim is to cut down the blood flowing into that system. The drugs that achieve splanchnic vasoconstriction are vasoactive agents such as somatostatin, its analogue octreotide, terlipressin and vasopressin. Among the four choices offered, octreotide is the somatostatin analogue, and it directly reduces splanchnic and portal blood flow, making it the established medical agent for acute variceal hemorrhage, usually given alongside endoscopic band ligation and prophylactic antibiotics. Looking at the alternatives: pantoprazole suppresses gastric acid and helps ulcer-related upper GI bleeding but does nothing for portal pressure; desmopressin boosts von Willebrand factor for bleeding disorders; and somatotropin is growth hormone with no hemostatic indication. Therefore the single appropriate answer for medical management of variceal bleeding is octreotide.\[\boxed{\text{Octreotide}}\]