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stochastic_claims_demo.jl
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### A Pluto.jl notebook ###
# v0.19.9
using Markdown
using InteractiveUtils
# ╔═╡ 77b330b5-9fb7-4f74-8306-b147bf052dae
begin
using CSV, DataFrames
using MortalityTables, ActuaryUtilities
using Dates
using ThreadsX
using BenchmarkTools
end
# ╔═╡ a7b52cf6-b03d-47e9-818c-22ea8f82f158
using Random
# ╔═╡ 8b86fb4e-2835-4282-8345-6708033423f1
using UnicodePlots
# ╔═╡ c1cacc0f-a789-4fd6-8f1e-a822dd17a66e
md" # Stochastic claims projections demo"
# ╔═╡ 9abe410a-8f6b-4d66-ac0e-570df1e34b47
md" Define a datatype. Not strictly necessary, but will make extending the program with more functions easier."
# ╔═╡ 11f171f8-9137-4e53-9384-f302ad3a773c
md"Type annotations are optional, but providing them is able to coerce the values to be all plain bits (i.e. simple, non-referenced values like arrays are) when the type is constructed. This makes the whole data be stored in the stack and is an example of data-oriented design. It's much slower without the type annotations (~0.5 million policies per second, ~50x slower)"
# ╔═╡ 4310ba76-2a79-49e9-b9c4-78e82871184f
begin
@enum Sex Female = 1 Male = 2
@enum Risk Standard = 1 Preferred = 2
end
# ╔═╡ f4d57736-ad94-4139-a372-dc281be9303a
struct Policy
id::Int
sex::Sex
benefit_base::Float64
COLA::Float64
mode::Int
issue_date::Date
issue_age::Int
risk::Risk
end
# ╔═╡ be3ae4ef-661c-40b1-acce-4591cc7e6e5f
md"Load the data:"
# ╔═╡ 14901845-d99b-4a26-947d-63f4c8dd8334
sample_csv_data =
IOBuffer(
raw"id,sex,benefit_base,COLA,mode,issue_date,issue_age,risk
1,M,100000.0,0.03,12,1999-12-05,30,Std
2,F,200000.0,0.03,12,1999-12-05,30,Pref"
)
# ╔═╡ 5ee1ca24-45aa-47e7-a948-26b4cc819cdb
policies = let
# read CSV directly into a dataframe
# df = CSV.read("sample_inforce.csv",DataFrame) # use local string for notebook
df = CSV.read(sample_csv_data,DataFrame)
# map over each row and construct an array of Policy objects
map(eachrow(df)) do row
Policy(
row.id,
row.sex == "M" ? Male : Female,
row.benefit_base,
row.COLA,
row.mode,
row.issue_date,
row.issue_age,
row.risk == "Std" ? Standard : Preferred,
)
end
end
# ╔═╡ 89997227-faa5-45fa-aabb-304dee864fd3
md" Define what mortality gets used:"
# ╔═╡ e8d3578b-560b-491e-8ceb-85057f18373e
mort = Dict(
Male => MortalityTables.table(988).ultimate,
Female => MortalityTables.table(992).ultimate,
)
# ╔═╡ febebebd-48e6-4645-9c21-699bfb50eb3a
function mortality(pol::Policy,params)
return params.mortality[pol.sex]
end
# ╔═╡ 23dec098-dda1-4153-bc3f-e1816354888b
md" This defines the core logic of the policy projection and will write the results to the given `out` container (here, a named tuple of arrays).
This is using a threaded approach where it could be operating on any of the computer's available threads, thus acheiving thread-based parallelism (as opposed to multi-processor (multi-machine) or GPU-based computation which requires formulating the problem a bit differently (array/matrix based). For the scale of computation here, I think I'd apply this model of parallelism."
# ╔═╡ ef0b652f-4f73-463a-be25-2e0466286ce1
function pol_project!(out,policy,params)
# some starting values for the given policy
dur = duration(policy.issue_date,params.val_date)
start_age = policy.issue_age + dur - 1
COLA_factor = (1+policy.COLA)
cur_benefit = policy.benefit_base * COLA_factor ^ (dur-1)
# get the right mortality vector
qs = mortality(policy,params)
# grab the current thread's id to write to results container without conflicting with other threads
tid = Threads.threadid()
ω = lastindex(qs)
# inbounds turns off bounds-checking, which makes hot loops faster but first write loop without it to ensure you don't create an error (will crash if you have the error without bounds checking)
@inbounds for t in 1:min(params.proj_length,ω - start_age)
q = qs[start_age + t] # get current mortality
if (rand() < q)
return # if dead then just return and don't increment the results anymore
else
# pay benefit, add a life to the output count, and increment the benefit for next year
out.benefits[t,tid] += cur_benefit
out.lives[t,tid] += 1
cur_benefit *= COLA_factor
end
end
end
# ╔═╡ c3e16d9b-af03-4608-b982-c1c99e638e2d
md" Parameters for our projection:"
# ╔═╡ 8ebc2609-576a-4105-aabe-84f1fe51e8de
params = (
val_date = Date(2021,12,31),
proj_length = 100,
mortality = mort,
)
# ╔═╡ b2f183d5-c739-467f-8e77-2546fff33c0c
md" Check the number of threads we're using:"
# ╔═╡ 84b2c368-c1ba-41ed-ab7c-9677a7293f1a
Threads.nthreads()
# ╔═╡ 055c5cc1-0cf3-407a-af4f-057bc2b8d0e8
function project(policies,params)
threads = Threads.nthreads()
benefits = zeros(params.proj_length,threads)
lives = zeros(Int,params.proj_length,threads)
out = (;benefits,lives)
ThreadsX.foreach(policies) do pol
pol_project!(out,pol,params)
end
map(x->vec(reduce(+,x,dims=2)),out)
end
# ╔═╡ 51bdd873-32db-494e-a2f2-1975124f8008
md" Example of single projection:"
# ╔═╡ cfe6a86d-a48e-497c-8a7a-837b16a41931
project(repeat(policies,100_000),params)
# ╔═╡ 8c87a09a-c46f-4143-b2c7-87c51a54332c
md" ## Benchmarking"
# ╔═╡ bde3cee6-8b59-42f8-b450-10044636a563
md"
Using a Macbook Air laptop, about 30 million policies able to be stochastically projected per second:
"
# ╔═╡ e087efbc-9a9f-4e09-ac14-2e4067de458b
let
policies_to_benchmark = 3_000_000
# adjust the `repeat` depending on how many policies are already in the array
# to match the target number for the benchmark
n = policies_to_benchmark ÷ length(policies)
@benchmark project(p,r) setup=(p=repeat($policies,$n);r=$params)
end
# ╔═╡ 9e45b261-4e29-48d7-99fe-1fc623b5a757
md""" ## Stochastic Set
Loop through and calculate the reults `n` times (this is only running the two policies in the sample data" `n` times).
"""
# ╔═╡ 778f030b-aab1-4191-8902-3f10f402b82e
function stochastic_proj(policies,params,n)
ThreadsX.map(1:n) do i
project(policies,params)
end
end
# ╔═╡ 73ead2b9-733d-470c-a863-9aa4397c35cd
stoch = stochastic_proj(policies,params,1000)
# ╔═╡ 0e8d3fe0-5df3-4db9-88a6-fe4f738211c0
let
v = [pv(0.03,s.benefits) for s in stoch]
histogram(v,nbins=15)
end
# ╔═╡ 786312c8-2a40-44db-96cd-a1edc2f29e9a
md" # Further Optimization
In no particular order:
- the RNG could be made faster: https://bkamins.github.io/julialang/2020/11/20/rand.html
- Could make the stochastic set distributed, but at the current speed the overhead of distributed computing is probably more time than it would save. Same thing with GPU projections
- ...
"
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
ActuaryUtilities = "bdd23359-8b1c-4f88-b89b-d11982a786f4"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
ThreadsX = "ac1d9e8a-700a-412c-b207-f0111f4b6c0d"
UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"
[compat]
ActuaryUtilities = "~3.2.0"
BenchmarkTools = "~1.3.1"
CSV = "~0.10.4"
DataFrames = "~1.3.4"
MortalityTables = "~2.3.0"
ThreadsX = "~0.1.10"
UnicodePlots = "~2.11.2"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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