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Capital_Allocation.jl
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Capital_Allocation.jl
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### A Pluto.jl notebook ###
# v0.17.7
using Markdown
using InteractiveUtils
# ╔═╡ f826d106-7feb-11ec-2985-7946caa5d5e6
using Distributions
# ╔═╡ ddaece16-03b5-4e43-bee7-23b8142ecbe9
using ActuaryUtilities
# ╔═╡ 9e843758-6371-49b4-bf9d-8cb096ce1d8b
using Plots
# ╔═╡ 11f63e55-3dc5-4c71-acc0-3136a874af31
md"[based on this paper](https://www.soa.org/globalassets/assets/files/resources/essays-monographs/2007-erm-symposium/m-as07-1-03.pdf)"
# ╔═╡ e413b125-446e-4995-91b0-1581823f031f
function loss()
fire = rand() < 0.25 ? rand(Exponential(4)) : 0
wind = rand() < 0.05 ? rand(Exponential(20)) : 0
earthquake = rand() < 0.01 ? rand(Exponential(100)) : 0
return [fire,wind, earthquake]
end
# ╔═╡ fefc9546-52a2-4691-99cb-9417ae63b1d7
function loss2()
wind = rand() < .19 ? 99 : 0
earthquake = rand() < .04 ? 100 : 0
return [wind,earthquake]
end
# ╔═╡ 71a1aed9-9c3f-42f5-b6ad-bfeaf6b27d27
sims = [loss() for _ in 1:10000]
# ╔═╡ e36563fd-8134-4f5e-9215-e74d60151758
sims2 = [loss2() for _ in 1:10000]
# ╔═╡ 48a1cbb8-7043-40de-a6b4-c682b1a1a061
"""
Return the percentile layer of capital
Percentile Layer of Capital (α, α + j) = Required Capital at percentile (α + j) – Required Capital at percentile (α)
"""
function layer_of_capital(losses,capital_function,α,j=0.01)
loss_totals = sum.(sims)
rc1 = capital_function(loss_totals,α)
rc2 = capital_function(loss_totals,α+j)
return rc2 - rc1
end
# ╔═╡ 603acf00-6584-46a9-aa32-2926acbc179f
# ╔═╡ b1035176-ac37-4fff-8afa-eb313e6d40cf
layer_of_capital(sims,VaR,.99)
# ╔═╡ 7ded16b2-a161-4e6b-8616-84c3fd7a8537
VaR(sum.(sims),.99)
# ╔═╡ b14db721-fd8d-4009-a9f9-ab58b599b0d8
# ╔═╡ e5182d70-9fd9-4d56-8f1b-ec37c7ceddb5
"""
Return the percentile layer of capital
Percentile Layer of Capital (α, α + j) = Required Capital at percentile (α + j) – Required Capital at percentile (α)
"""
function capital_allocation(losses,capital_function,α,j=0.01)
loss_totals = sum.(sims)
capitalₐ = capital_function(loss_totals,α)
capitalₖ = capital_function(loss_totals,α+j)
@show ∇ = capitalₖ - capitalₐ
layer = (loss_totals .>= capitalₐ) .& (loss_totals .<= capitalₖ)
denom = sum(loss_totals .> capitalₐ) / length(loss_totals)
# Allocation of capital on layer [x(α+j) – x(α)] to loss event x(i) =
# [x(α+j) – x(α)] * Probability ( x = x(i) ) / Probability ( x > x(α) )
# Sum across all layers of capital such that α ≥ 0, (α+j) ≤ min(i, k)
# Note the min(i, k) restriction. For any loss event, we sum across all layers of capital up to the amount of the given loss event, but not if the loss event exceeds the VaR threshold. In such a case, the loss beyond the VaR threshold does not generate additional allocated capital to the loss event.
allocation = map(1: length(first(losses))) do i
pᵢ = sum(min(l[i],∇) for l in losses[layer])
end
return allocation ./ ∇
end
# ╔═╡ beb322d2-4e26-4868-ba40-a139e7f88a60
# ╔═╡ 5b0a3bbd-0446-4f1c-89d4-8928b0eb4f69
#TODO this doesn't tie with the table on pg 26
# need to correct `capital_allocation`
capital_allocation(sims,VaR,.99)
# ╔═╡ 09c2def4-af75-4c16-b90a-c6e76a7c2269
VaR(sum.(sims2),.99)
# ╔═╡ 2be442e3-150d-4c19-b5de-793bd3fe0988
bar(sort!(sum.(sims2)))
# ╔═╡ 66877355-56d1-434d-ab62-a319c31154f7
plot(sort(sum.(sims)))
# ╔═╡ b64b5af7-ebdf-4c5f-a4fa-af781c363e8e
capital_allocation(sims2,VaR,.99)
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
ActuaryUtilities = "bdd23359-8b1c-4f88-b89b-d11982a786f4"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
[compat]
ActuaryUtilities = "~2.8.0"
Distributions = "~0.25.41"
Plots = "~1.25.7"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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