Person列中可能存在多个Person的解：

df = pd.DataFrame([{'Person': 'Mr. Bun', 'Company': 'Company A', 
                    'Begin date': '8/1984', 'End Date': '10/1984'}, 
                   {'Person': np.nan, 'Company': 'Company B',
                    'Begin date': '1/1985', 'End Date': '3/1985'}])
    
print (df)
    Person    Company Begin date End Date
0  Mr. Bun  Company A     8/1984  10/1984
1      NaN  Company B     1/1985   3/1985

#forward filling missing values
df['Person'] = df['Person'].ffill()

#convert values to months periods
df['Begin date'] = pd.to_datetime(df['Begin date']).dt.to_period('m')
df['End Date'] = pd.to_datetime(df['End Date']).dt.to_period('m')

#repeat indices for difference of End and Begin months periods
df1 = df.loc[df.index.repeat(df['End Date'].astype(int)
                     .sub(df['Begin date'].astype(int)).add(1))]

#add counter to Begin date
df1['Year'] = df1['Begin date'].add(df1.groupby(level=0).cumcount())

#add Unemployed values for missing months
f = lambda x: x.reindex(pd.period_range(x.index.min(), x.index.max(), 
                                        freq='m', name='Year'), fill_value='Unemployed')
df1 = df1.set_index('Year').groupby('Person')['Company'].apply(f).reset_index()

#original format MM/YYYY
df1['Year'] = df1['Year'].dt.strftime('%m/%Y')

print (df1)
    Person     Year     Company
0  Mr. Bun  08/1984   Company A
1  Mr. Bun  09/1984   Company A
2  Mr. Bun  10/1984   Company A
3  Mr. Bun  11/1984  Unemployed
4  Mr. Bun  12/1984  Unemployed
5  Mr. Bun  01/1985   Company B
6  Mr. Bun  02/1985   Company B
7  Mr. Bun  03/1985   Company B

基本上，您可以使用类似下面的代码来加快处理速度：
数据：

df = pd.DataFrame({'name':['Bun', 'Bun'],
                   'comp':['A', 'B'],
                   'start': pd.to_datetime(['1984-08-31', '1985-01-31']),
                   'end':pd.to_datetime(['1984-10-31', '1985-03-31'])})

创建new Dataframe 以填充所有日期

new = df[['name', 'start']].set_index(['name', 'start'])
mux = pd.MultiIndex.from_product([new.index.levels[0], pd.date_range(start='1984-08-31', end='1985-03-31', freq='M')], names=['name', 'date'])
new.reindex(mux).reset_index()

其输出应为：

name       date
0  Bun 1984-08-31
1  Bun 1984-09-30
2  Bun 1984-10-31
3  Bun 1984-11-30
4  Bun 1984-12-31
5  Bun 1985-01-31
6  Bun 1985-02-28
7  Bun 1985-03-31

之后，可以将merge与df合并，然后删除不必要的行