from dataclasses import replace

import numpy as np
import pandas as pd
import plotly.io as pio

from _example.notebook.helper_funcs import (append_curves_to_structure_df,
                                            df_to_classes, get_xs_freqs,
                                            plot_xs_freqs, print_layer_results,
                                            process_curve_df, show_tree_chart)
from repy.distributions import Lognormal
from repy.exposure import (Curve, PAndCClassAssumptions, PAndCClassTree,
                           PAndCExposureAnalysis, PDLGDClassAssumptions,
                           PDLGDClassTree, PDLGDExposureAnalysis)

pd.options.display.float_format = (lambda x: f'{x:.2%}' if abs(x) <= 1
                                   else f'{x:,.2f}')

pio.renderers.default = 'notebook_connected'

Treaty Background

Cedant writes 5 lines of Casualty business:

  • D&O
    • Costs Included
  • E&O
    • Costs Included
  • Med Mal
    • Costs In Addition
  • GL
    • Costs In Addition
  • Workers' Comp
    • Costs In Addition

Cedant writes 10m maximum line. In the example data, the following are written for each LOB:

  • 1m primary acceptances, written 100%
  • 4m xs 1m acceptances, written 75%
    • "Supported excess", stacks with the primary
  • 15m xs 5m acceptances, written 40%
    • "Supported excess", stacks with the primary and 4m xs 1m
  • 10m xs 10m acceptances, written 50%
    • "Unsupported Excess", does not stack

The treaty layers are as follows:

  • 1m xs 1m
  • 3m xs 2m
  • 5m xs 5m

The costs treatment for the treaty layers follows the underlying policies

  • Included -> Included
  • In Addition -> Pro Rata In Addition

Analysis 1: LOBs as Modelling Classes

Analysis Structure

Exposure Curves

# Read curves in we intend to use.
raw_curve_df = pd.read_csv('_example/notebook/curves.csv', index_col='analysis_cls')
curve_df = process_curve_df(raw_curve_df)
curve_df
curve_type curve_params curve_inc_alae severity_scale
analysis_cls
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# Form Curves and store in dict.
# Note last last 2 columns in curve DataFrame are optional kwargs.
curve_dict = df_to_classes(curve_df, Curve,
                           optional_kwargs=['curve_inc_alae', 'severity_scale'])
curve_dict

{'D&O': Curve(curve_type='Lognormal', curve_params=[12, 2], curve_inc_alae=True, severity_scale=1.25),
 'E&O': Curve(curve_type='Pareto', curve_params=[1000000.0, 1.8], curve_inc_alae=False, severity_scale=1.0),
 'Med Mal': Curve(curve_type='UserILFs', curve_params=[(1000000.0, 2000000.0, 5000000.0, 10000000.0, 20000000.0), (1, 1.5, 1.7, 1.8, 1.85)], curve_inc_alae=False, severity_scale=1.0),
 'GL': Curve(curve_type='MixedExponential', curve_params=[(10000.0, 1000000.0, 10000000.0), (0.6, 0.3, 0.1)], curve_inc_alae=False, severity_scale=1.0),
 'Workers Comp': Curve(curve_type='ELPPFs', curve_params=[(1000000.0, 2000000.0, 5000000.0, 10000000.0, 20000000.0), (0.2, 0.08, 0.03, 0.015, 0.01)], curve_inc_alae=False, severity_scale=1.0)}
# Curves take array-like inputs and use broadcasting.
Lognormal.lev(1e6, np.array([12, 12.5, 13]).reshape((-1, 1)),
              [2, 2.5, 3])

array([[347196.82745759, 374799.04776828, 394339.63813165],
       [433316.8583742 , 447185.68394235, 456384.89301557],
       [523696.0825669 , 521766.85523259, 519691.97689529]])

Remaining Structural Elements

# Read in analysis class structure details.
structure_df = pd.read_csv('_example/notebook/structure.csv',
                           index_col='analysis_cls')
structure_df
glr glr_includes_alae prm_prospective pol_costs ri_costs alae_pc_indemnity
analysis_cls
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# Insert column with curves for each analysis class.
# Each entry is [(curve, weight)].
# In this first example, each class has a single curve with 100% weight.
append_curves_to_structure_df(structure_df, curve_dict)
structure_df
glr glr_includes_alae prm_prospective pol_costs ri_costs alae_pc_indemnity curves
analysis_cls
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# Form dict of analysis class assumptions.
analysis_cls_dict = df_to_classes(structure_df, PAndCClassAssumptions,
                                  optional_kwargs=['alae_pc_indemnity'])
analysis_cls_dict

{'D&O': PAndCClassAssumptions(curves=[(Curve(curve_type='Lognormal', curve_params=[12, 2], curve_inc_alae=True, severity_scale=1.25), 1)], glr=0.6, prm_prospective=10000000.0, glr_includes_alae=True, alae_pc_indemnity=0.3, pol_costs='Included Within Limit', ri_costs='Included'),
 'E&O': PAndCClassAssumptions(curves=[(Curve(curve_type='Pareto', curve_params=[1000000.0, 1.8], curve_inc_alae=False, severity_scale=1.0), 1)], glr=0.55, prm_prospective=8000000.0, glr_includes_alae=True, alae_pc_indemnity=0.1, pol_costs='Included Within Limit', ri_costs='Included'),
 'Med Mal': PAndCClassAssumptions(curves=[(Curve(curve_type='UserILFs', curve_params=[(1000000.0, 2000000.0, 5000000.0, 10000000.0, 20000000.0), (1, 1.5, 1.7, 1.8, 1.85)], curve_inc_alae=False, severity_scale=1.0), 1)], glr=0.7, prm_prospective=9000000.0, glr_includes_alae=True, alae_pc_indemnity=0.05, pol_costs='In Addition', ri_costs='PRIA'),
 'GL': PAndCClassAssumptions(curves=[(Curve(curve_type='MixedExponential', curve_params=[(10000.0, 1000000.0, 10000000.0), (0.6, 0.3, 0.1)], curve_inc_alae=False, severity_scale=1.0), 1)], glr=0.65, prm_prospective=10000000.0, glr_includes_alae=True, alae_pc_indemnity=0.05, pol_costs='In Addition', ri_costs='PRIA'),
 'Workers Comp': PAndCClassAssumptions(curves=[(Curve(curve_type='ELPPFs', curve_params=[(1000000.0, 2000000.0, 5000000.0, 10000000.0, 20000000.0), (0.2, 0.08, 0.03, 0.015, 0.01)], curve_inc_alae=False, severity_scale=1.0), 1)], glr=0.8, prm_prospective=7000000.0, glr_includes_alae=True, alae_pc_indemnity=0.05, pol_costs='In Addition', ri_costs='PRIA')}
# Form analysis structure.
# This is of hierarchical tree form, although in this first example we
# just have root and leaves, no branches.
structure = PAndCClassTree.as_flat_classes(analysis_cls_dict)

Exposure Listing

# Read policy data.
df = pd.read_csv('_example/notebook/policy_data.csv')
df
stack_id cls_id lim xs share prm user_description
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Rate Layers

analysis = PAndCExposureAnalysis(df, structure)
layers = [(1e6, 1e6), (3e6, 2e6), (5e6, 5e6)]
analysis.rate(layers)

Results by Layer

print_layer_results(display, analysis, layers)
pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 1
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pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 2
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pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 3
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show_tree_chart(analysis, 2)

Excess Frequencies

xs_freqs = get_xs_freqs(analysis, start=1e6, stop=10e6)
xs_freqs
Threshold Analysis Analysis - Med Mal Analysis - E&O Analysis - D&O Analysis - GL Analysis - Workers Comp
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plot_xs_freqs(xs_freqs)

Analysis 2: Hierarchical Classes

In this extension of the example, the cedant now writes property (10m primary policies, written 100%), as well as casualty.

Furthermore, for the E&O casualty LOB, we become aware that the cedant is reweighting its book, writing greater unsupported excess. Hence, for E&O, we wish to split our analysis into Unsupported Excess and "Other" business.

Analysis Structure

# Create property curve.
curve_property = Curve(curve_type='UserFLS', curve_params=[
    [0, 0.1, 0.9, 1], [0, 0.8, 0.99, 1]
])

# Form property analysis class data.
property_data = PAndCClassAssumptions(
    curves=[(curve_property, 1)], glr=0.4, prm_prospective=50e6
)

# Form modified analysis class data for E&O, now we're splitting the class.
eo_unsupported_data = replace(structure['E&O'].data, prm_prospective=2e6)
eo_other_data =  replace(structure['E&O'].data, prm_prospective=6e6)

# Form a hierarchical analysis class tree.
# Most of our rating assumptions stay as before, but we add property
# and apportion the prospective premium into the 2 subclasses for E&O.

# cls_ids 1, 2, ...
structure_dict = {
    ('Casualty', 'D&O'): structure['D&O'].data,
    ('Casualty', 'E&O', 'Other'): eo_other_data,
    ('Casualty', 'Med Mal'): structure['Med Mal'].data,
    ('Casualty', 'GL'): structure['GL'].data,
    ('Casualty', 'Workers Comp'): structure['Workers Comp'].data,
    ('Property',): property_data,  # id 6.
    ('Casualty', 'E&O', 'Unsupported Excess'): eo_unsupported_data,  # id 7.
}

structure = PAndCClassTree.from_leaves(structure_dict)

Exposure Listing

# We can modify our existing listing by adding a line for the property
# exposure, making sure to stamp it with cls_id 6.
property_row = pd.DataFrame({
    'stack_id': [9999],  # No stacking with existing exposures.
    'cls_id': 6,  # Matching structure, above.
    'lim': 10e6,
    'xs': 0,
    'share': 1,
    'prm': 6.5e6,
    'user_description': 'Property'
})
df = pd.concat([df, property_row], ignore_index=True)
df
stack_id cls_id lim xs share prm user_description
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# Our policy listing currently has cls_id 2 allocated to both
# "Unsupported Excess" and "Other".
# We need to change the unsupported excess rows to cls_id 7.
unsupported_xs_mask = (df['cls_id'] == 2) & (df['lim'] == 10e6)
df.loc[unsupported_xs_mask, 'cls_id'] = 7
df
stack_id cls_id lim xs share prm user_description
Loading... (need help?)

Rate Layers

analysis = PAndCExposureAnalysis(df, structure)
analysis.rate(layers)

Results by Layer

print_layer_results(display, analysis, layers)
pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 1
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pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 2
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pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 3
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show_tree_chart(analysis, 2)

# We can add results from any leaf nodes we desire using '+' operator.
analysis.results(1)['Property'].data + \
    analysis.results(1)[('Casualty', 'E&O', 'Unsupported Excess')].data

PAndCStats(pro_rata_rate=0.10384615384615385, ltlr=0.03184435155304396, xs_rate=0.014088912584943419, prm_profiled=6700000.0, prm_prospective=52000000.0)
# We can see full row-by-row calcs that generated these results.
# analysis.expos_calcs

Excess Frequencies

xs_freqs = get_xs_freqs(analysis, start=1e6, stop=10e6)
xs_freqs
Threshold Analysis Analysis - Casualty - Workers Comp Analysis - Casualty - E&O Analysis - Casualty - GL Analysis - Casualty - Med Mal Analysis - Property Analysis - Casualty - E&O - Other Analysis - Casualty - D&O Analysis - Casualty - E&O - Unsupported Excess Analysis - Casualty
Loading... (need help?)
plot_xs_freqs(xs_freqs)

Analysis 3: Weighted Curves

In this extension of example 2, we wish to use a State-split for the GL line of business. We will simplify here and assume only two States, each with is own exposure curve.

Analysis Structure

# We now have 2 curves for GL. First as before, 10% weight.
curve_gl_weighted_1 = Curve(curve_type='MixedExponential', curve_params=[
    [10e3, 1e6, 10e6], [0.6, 0.3, 0.1]
])

# Make second curve severe first-loss-scale, 90% weight.
curve_gl_weighted_2 = Curve(curve_type='Swiss', curve_params=0.1)

curves_gl = [(curve_gl_weighted_1, 0.1), (curve_gl_weighted_2, 0.9)]

# Replace curves in our structure.
structure_dict[('Casualty', 'GL')] = replace(structure_dict[('Casualty', 'GL')],
                                             curves=curves_gl)
structure = PAndCClassTree.from_leaves(structure_dict)

Rate Layers

analysis = PAndCExposureAnalysis(df, structure)
analysis.rate(layers)

Results by Layer

print_layer_results(display, analysis, layers)
pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 1
Loading... (need help?)
pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 2
Loading... (need help?)
pro_rata_rate ltlr xs_rate prm_profiled prm_prospective prospective_xs_prm
Layer 3
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show_tree_chart(analysis, 2)

Excess Frequencies

xs_freqs = get_xs_freqs(analysis, start=1e6, stop=10e6)
xs_freqs
Threshold Analysis Analysis - Property Analysis - Casualty - GL Analysis - Casualty - Med Mal Analysis - Casualty - E&O - Unsupported Excess Analysis - Casualty - E&O - Other Analysis - Casualty Analysis - Casualty - Workers Comp Analysis - Casualty - E&O Analysis - Casualty - D&O
Loading... (need help?)
plot_xs_freqs(xs_freqs)

Analysis 4: Credit / Surety

np.random.seed(42)

df = pd.DataFrame({
    'cls_id': [1, 2, 3] * 3_333 + [1],
    'lim': np.random.choice([1e6, 20e6, 100e6], 10_000, p=[0.1, 0.89, 0.01]),
    'pd': np.random.choice([0.01, 0.1], 10_000, p=[0.9, 0.1]),
    'lgd_mean': np.random.choice([0.06, 0.2], 10_000),
    'lgd_cov': np.random.uniform(0.3, 0.6, 10_000)
})
df
cls_id lim pd lgd_mean lgd_cov
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structure = PDLGDClassTree.from_leaves({
    ('Credit', 'WTO'): PDLGDClassAssumptions(prm_prospective=30e6),
    ('Credit', 'Structured'): PDLGDClassAssumptions(prm_prospective=30e6),
    ('Surety',): PDLGDClassAssumptions(prm_prospective=20e6)
})

analysis = PDLGDExposureAnalysis(df, structure)
layers = [(10e6, 10e6), (30e6, 20e6)]
analysis.rate(layers)
print_layer_results(display, analysis, layers)
xs_prm xs_rate prm_prospective
Layer 1
Loading... (need help?)
xs_prm xs_rate prm_prospective
Layer 2
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xs_freqs = get_xs_freqs(analysis, start=10e6, stop=100e6)
xs_freqs
Threshold Analysis Analysis - Surety Analysis - Credit - WTO Analysis - Credit - Structured Analysis - Credit
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plot_xs_freqs(xs_freqs)