ruin-theory

A small model implementing basic Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process or Poisson risk process)

Initialization

Class Model describes all model-related features. Use Model() to create its instance.

model = Model(u_initial=20, c=15.5, rate=3, mu=2.7, t_end=50)

u_initial - initial company capital.
c - premium rate.
rate - rate of insurance cases.
mu - mean of insurance payments.
t_end - upper bound of the time interval (lower is 0).

Trajectories

Use plot_trajectories to visualize the risk process. Pass Model instance and filename as parameters.

from plot import plot_trajectories
plot_trajectories(model, 'model_1.png')

Basic Monte Carlo

Use basic_monte_carlo to compute the RUIN probability using brute-force Monte Carlo method. Pass Model instance and examples amount as parameters.

from estimate import basic_monte_carlo
ruin_probability = basic_monte_carlo(model, examples=100)

Advanced Monte Carlo

Use advanced_monte_carlo to compute the RUIN probability using integrated tail distribution. Pass Model instance and examples amount as parameters.

from estimate import advanced_monte_carlo
ruin_probability = advanced_monte_carlo(model, examples=1000)

Inverse Laplace Transform

Use get_ilt_first or get_ilt_second respectively to figure out the true SURVIVAL probability, using the numeric approximation of the inverse Laplace transform. Pass u initial capital argument to pass to inverse transform.

from ilt import get_ilt_first, get_ilt_second
survival_probability_first = get_ilt_first(10)
survival_probability_second = get_ilt_second(50)

Maths

Preliminary mathematical derivations and justifications can be found in here.