Knowledge is the Only Good


import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from aggregate import build, qd, Distortion, Portfolio #, knobble_fonts

# knobble_fonts(True)

def my_ff(x):
  """My float formatter."""
  try:
    if x == int(x):
      return f'{x:,d}'
    elif abs(x) < 0.005:
      return f'{x:.5g}'
    elif abs(x) < 100:
      return f'{x:.3f}'
    else:
      return f'{x:,.0f}'
  except:
    return str(x)

pd.options.display.float_format = my_ff

from IPython.display import HTML, display
from greater_tables import GT

__gt_global = GT()

def nothing(df):
    return df

sd = sdp = nothing

#from greater_tables import qd

# try:
#     from greater_tables import qd
# except ModuleNotFoundError:
#     print('Greater tables not found...using IPython.display.')
#     qd = display

#sd = qd
#sdp = qd

#def sd(df):
#    # return df
#    bit =  df.style.format(formatter=lambda x: #f'{x:.4g}').set_properties(**{'text-align': 'right'})
#    print(bit.to_html())
#    return bit
#
#def sdp(df):
#    # return df
#    bit = df.style.format(formatter=lambda x: #f'{x:.1%}').set_properties(**{'text-align': 'right'})
#    print(bit.to_html())
#    return bit

gcn_namer = {'X2': 'X2 net', 'X3': 'X2 ceded', 'X': 'X2', 'X4': 'X2'}

def gcn(df):
    bit = df.loc[['X2', 'X3']]
    df.loc['X', :] = bit.sum(0)
    df.loc['X', 'LR'] = df.loc['X', 'L'] / df.loc['X', 'P']
    df.loc['X', 'PQ'] = df.loc['X', 'P'] / df.loc['X', 'Q']
    df.loc['X', 'COC'] = df.loc['X', 'M'] / df.loc['X', 'Q']
    df = df.rename(index=gcn_namer)
    df = df.sort_index()
    return df

wgs = pd.DataFrame(
    {
        'X1': [36, 40, 28, 22, 33, 32, 31, 45, 25, 25],
        'X2': [ 0,  0,  0,  0,  7,  8,  9, 10, 40, 40],
        'X3': [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 35],
        'p_total': 1/10
    }
)

wport = Portfolio.create_from_sample('WGS', wgs, bs=1, log2=8)
wport.calibrate_distortions(Ps=[1], COCs=[.15])
ans = wport.price(1, allocation='linear')

PLOT_FACE_COLOR = 'white'  # '#e9e9f2'   # 'lightsteelblue'
FIGURE_BG_COLOR = '#e9e9f2'  # '#262680'   # 'aliceblue'
plt.rcParams.update({
    "axes.edgecolor": "black",
    "axes.facecolor": PLOT_FACE_COLOR,
    "axes.labelcolor": "black",
    "figure.dpi": 150,
    "figure.facecolor": FIGURE_BG_COLOR,
    "font.family": "sans-serif",
    "font.size": 10,
    "legend.edgecolor": "none",
    "legend.facecolor": PLOT_FACE_COLOR,
    "legend.labelcolor": "black",
    "text.color": 'black',  # "white",
    "xtick.color": 'black', #"white",
    "ytick.color": 'black', #"white",
})

wport.dists

{'ccoc': ccoc, 'ph': ph, 'wang': wang, 'dual': dual, 'tvar': tvar}

fig, axs = plt.subplots(1, 5, figsize=(5*2, 2), constrained_layout=True, sharey=True)
xs = np.linspace(0, 1, 101)
for (k, v), ax in zip(wport.dists.items(), axs.flat):
    if k == 'ccoc':
        ax.plot([0,1], [1/1.15]*2)
        ax.plot(1, 2, 'r*')
    else:
        ax.plot(xs, v.g_prime(xs[::-1]))
    ax.plot([0, 1], [1,1], lw=.5, c='k')
    ax.set(title=k, ylim=[-0.05, 2.5], xlabel='Percentile')
    if ax is axs[0]:
        ax.set(ylabel='Weight adjustment')

colors

{0: 'Cccoc', 1: 'Cph', 2: 'Cwang', 3: 'Cdual', 4: 'Ctvar'}

fig, axs = plt.subplots(1, 2, figsize=(2*3, 3), constrained_layout=True, sharey=True)
ax0, ax1 = axs.flat
ps = np.linspace(0, 1, 1001)

colors = {k: f'C{i}' for i, k in enumerate(wport.dists.keys())}

ax = ax0
for (k, v) in wport.dists.items():
    ax.plot(ps, v.g(ps), lw=1, label=k, c=colors[k])
ax.set(aspect='equal')  
ax.legend(loc='upper left')

ccoc = wport.dists['ccoc']
tvar = wport.dists['tvar']
min_g = Distortion.minimum([ccoc, tvar])
colors[min_g.name] = 'k'

ax = ax1
for g in [ccoc, tvar, min_g]:
    ax.plot(ps, g.g(ps), lw=2 if g is min_g else 1, 
            ls='--' if g is min_g else '-',
            label=g.name, c=colors[g.name])
ax.set(aspect='equal')  
ax.legend(loc='upper left')

min_g.name

'minimum(2)'

wport

Portfolio object: WGS

Portfolio contains 3 aggregate components. Updated with bucket size 1, log2 = 8, validation: not unreasonable

		E[X]	Est E[X]	Err E[X]	CV(X)	Est CV(X)	Err CV(X)	Skew(X)	Est Skew(X)
unit	X
X1	Freq	1.0			0.0
	Sev	31.700	31.700	0.0	0.215	0.215	2.2204e-15	0.456	0.456
	Agg	31.700	31.700	0.0	0.215	0.215	2.2204e-15	0.456	0.456
X2	Freq	1.0			0.0
	Sev	11.400	11.400	2.2204e-16	1.299	1.299	-2.2204e-16	1.253	1.253
	Agg	11.400	11.400	2.2204e-16	1.299	1.299	-2.2204e-16	1.253	1.253
X3	Freq	1.0			0.0
	Sev	3.500	3.500	-2.2204e-16	3.0	3.000	2.2204e-16	2.667	2.667
	Agg	3.500	3.500	-2.2204e-16	3.0	3.000	2.2204e-16	2.667	2.667
total	Freq	3.0			0.0
	Sev	15.533	15.533	2.2204e-16	1.051			0.404
	Agg	46.600	46.600	-1.1102e-16	0.416	0.416	6.6613e-16	1.001	1.001

from aggregate.extensions.pir_figures import fig_10_5

fig_10_5(port=wport, x=60)

wport.distortion_df

			S	L	P	PQ	Q	COC	param	error
a	LR	method
100.0	0.870	ccoc	0.0	46.600	53.565	1.154	46.435	0.150	0.150	0.0
		ph	0.0	46.600	53.565	1.154	46.435	0.150	0.720	3.2978e-10
		wang	0.0	46.600	53.565	1.154	46.435	0.150	0.343	1.2525e-08
		dual	0.0	46.600	53.565	1.154	46.435	0.150	1.595	-3.3927e-07
		tvar	0.0	46.600	53.565	1.154	46.435	0.150	0.271	7.6102e-06

bit

	p_total	S	F
loss
22.0	0.100	0.900	0.100
28.0	0.100	0.800	0.200
36.0	0.100	0.700	0.300
40.0	0.400	0.300	0.700
55.0	0.100	0.200	0.800
65.0	0.100	0.100	0.900
100.0	0.100	0.0	1.0

wport.dists['ph'].shape

0.7204792831878889

bit = wport.density_df.query('p_total > 0')[['p_total','S']]
bit.index.name = 'loss'
bit = bit.rename(columns={'p_total': 'p'})
bit['gS'] = g.g(bit.S)
bit['q'] = -np.diff(bit.gS, prepend=1)
bit['dx'] = np.diff(bit.index, prepend=0)
bit0 = bit.copy()
bit.loc['Total', :] = [(bit0.p * bit0.index).sum(), 
                       (bit0.S.shift(1, fill_value=1) * bit0.dx).sum(),                                         (bit0.gS.shift(1, fill_value=1) * bit0.dx).sum(), 
                       (bit0.q * bit0.index).sum(), 
                       bit0.dx.sum()] 
bit

	p	S	gS	q	dx
loss
22.0	0.100	0.900	0.975	0.025	22.0
28.0	0.100	0.800	0.923	0.051	6.0
36.0	0.100	0.700	0.853	0.070	8.0
40.0	0.400	0.300	0.434	0.420	4.0
55.0	0.100	0.200	0.299	0.134	15.0
65.0	0.100	0.100	0.155	0.145	10.0
100.0	0.100	0.0	0.0	0.155	35.0
Total	46.600	46.600	53.565	53.565	100.0

bit0.S.shift(1, fill_value=1)

loss
22.0      1.0
28.0    0.900
36.0    0.800
40.0    0.700
55.0    0.300
65.0    0.200
100.0   0.100
Name: S, dtype: float64

(bit.q * bit.index).sum()

53.565217052032935

g.shape

1.5951514670652984