diff --git a/pypfopt/discrete_allocation.py b/pypfopt/discrete_allocation.py
index b5f5e35a..df6f6391 100644
--- a/pypfopt/discrete_allocation.py
+++ b/pypfopt/discrete_allocation.py
@@ -241,7 +241,9 @@ def greedy_portfolio(self, reinvest=False, verbose=False):
             # Calculate the equivalent continuous weights of the shares that
             # have already been bought
             current_weights = np.array(buy_prices) * np.array(shares_bought)
-            current_weights /= current_weights.sum()
+            invested = current_weights.sum()
+            if invested > 0:
+                current_weights /= invested
             ideal_weights = np.array([i[1] for i in self.weights])
             deficit = ideal_weights - current_weights
 
diff --git a/tests/test_discrete_allocation.py b/tests/test_discrete_allocation.py
index e5da0368..4fda59d7 100644
--- a/tests/test_discrete_allocation.py
+++ b/tests/test_discrete_allocation.py
@@ -7,6 +7,18 @@
 from tests.utilities_for_tests import get_data, setup_efficient_frontier
 
 
+@pytest.mark.parametrize("budget, expected, cash", [(100, {"B": 1}, 50), (10, {}, 10)])
+def test_greedy_portfolio_with_no_initial_shares(budget, expected, cash):
+    da = DiscreteAllocation(
+        {"A": 0.9, "B": 0.1}, pd.Series({"A": 1000.0, "B": 50.0}),
+        total_portfolio_value=budget,
+    )
+    with np.errstate(divide="raise", invalid="raise"):
+        allocation, leftover = da.greedy_portfolio()
+    assert allocation == expected
+    assert leftover == pytest.approx(cash)
+
+
 @pytest.mark.parametrize(
     "prices",
     [