Risk Pool

Create risk pools of assets with similar value and risk for insurance finance applications, such as insurance portfolios.

Features

• Create risk pool tables with step-by-step calculations
• See summary statistics about the risk pool, such as expected loss, standard deviation, premium and Value at Risk (VaR)
• Visualize the distribution of claim probabilities

Requirements & Usage

pip install numpy
pip install pandas
pip install matplotlib
pip install scipy

Copy the risk_pool.py file in your working directory.

Example

from risk_pool import RiskPool

There are 20 cottages, each valued at 50000 units of currency. The probability of a single cottage getting destroyed in a fire is 0.1 (asset losses are expected to be independent events):

# Risk pool parameters
number_of_assets = 20
asset_value = 50000
probability_of_loss = 0.1

# Using default p = 0.95 and multiplier = 1.00
rp = RiskPool(number_of_assets,asset_value,probability_of_loss)

The RiskPool class also has the following default parameters values:

• p = 0.95
  • This is the probability corresponding to the z-value of a normal distribution (confidence level). It adjusts VaR calculations.
• multiplier = 1.00
  • This is used to adjust risk tolerance levels; the higher the multiplier is, the higher the premium and VaR.

# Risk pool table
print(rp.table())

Number of claims	P(i)	Loss	P(i)*Loss	Sum of Squares Total	Number of outcomes
0	0.121577	0	0	3.03942e+06	1
1	0.27017	2500	675.43	1.68856e+06	20
2	0.28518	5000	1425.9	2.12306e-24	190
3	0.19012	7500	1425.9	1.18825e+06	1140
4	0.089779	10000	897.79	2.24447e+06	4845
5	0.031921	12500	399.02	1.79558e+06	15504
6	0.008867	15000	133.01	886704	38760
7	0.00197	17500	34.48	307883	77520
8	0.000356	20000	7.12	80049.7	125970
9	5.3e-05	22500	1.19	16141.7	167960
10	6e-06	25000	0.16	2576.82	184756
11	1e-06	27500	0.02	329.423	167960
12	0	30000	0	33.8912	125970
13	0	32500	0	2.80399	77520
14	0	35000	0	0.185388	38760
15	0	37500	0	0.00966992	15504
16	0	40000	0	0.000389404	4845
17	0	42500	0	1.16868e-05	1140
18	0	45000	0	2.4624e-07	190
19	0	47500	0	3.25125e-09	20
20	0	50000	0	2.025e-11	1

Explanation:

• Number of claims: the number of cottages destroyed in a fire in this example case
• P(i): the probability of having i number of claims
• Loss: the total loss corresponding to i number of claims
• P(i)*Loss: the weighted expected loss for i number of claims
• Sum of Squares Total: SST, a measure of variance of the loss distribution
• Number of outcomes: the number of ways that i number of claims can happen

# Risk pool summary statistics
print(rp.stats())

	Measure
Asset value	50000
P(loss)	0.1
Number of assets	20
Expected loss	5000
Stdev	3354.1
Z-score	1.64
Multiplier	1
Premium	250
VaR	-517.01

Explanation:

• Asset value: value of a single asset (cottage value)
• P(loss): probability of loss for a single asset (cottage burning down)
• Number of assets: the number of assets in the risk pool (total amount of cottages)
• Expected loss: the expected total loss of the risk pool
• Stdev: standard deviation; volatility of the risk pool
• Z-score: the z-score corresponding to the chosen confidence level (p = 0.95)
• Multiplier: premium and VaR adjustment factor (risk tolerance level)
• Premium: the amount that should be charged to cover potential losses
• VaR: Value at Risk, the loss in the worst case scenario at 95% confidence level (p = 0.95)

# Distribution of claim probabilities
print(rp.visualize())

The picture above shows that the most likely scenario involves two cottages getting destroyed in a fire. The chance for this is 28.52%, as seen also from the risk pool table.