Implement TrendConstant()

[kennethshsu]

Discussed in #506

^{Originally posted by vdunaway April 4, 2024}
Could someone please provide more details on how the multipart trending works, specifically the math behind what chainladder is doing and how to properly enter the dates for what you intend? I've been toggling the start/end dates and it's not working as intended, thus, potentially the documentation/user-guide could be enhanced regarding this.

For example, say I want to apply a multi-step trending that incorporates the following:

Trends for Year X-1 to X*
	Annual
Year	Trend Rate
Prior to 2021	3.5%
2021	10.0%
2023	5.0%
Trend To Date =	12/31/2024
*trend rate remains the same until
new trend in list

When I run through chainladder, I don't get what I was expecting. Am I inputting the dates incorrectly?

p = pd.DataFrame({'Year': list(range(2014,2024)), 'Premium': [10000]*10})
p_tri = cl.Triangle(p, origin='Year', columns='Premium', cumulative = True)

test = cl.Trend(
    trends=[.05, .1, .035],
    dates=[('2024-12-31', '2022'),('2022', '2020'),('2020','1990')]
).fit(p_tri).trend_

test
Out[71]: 
          2023
2014  1.661630
2015  1.605439
2016  1.551149
2017  1.498695
2018  1.448014
2019  1.399048
2020  1.278334
2021  1.162121
2022  1.102500
2023  1.050000

Dissecting the chainladder output and comparing to expectation, how would one enter the dates into cl.Trend() to obtain the expected result?

	Chainladder Output	Chainladder Resulting YoY Trend Factor	Expected YoY Trend Factor	Expected Result
2014	1.6616298	1.0350000	1.0350000	1.6398573
2015	1.6054394	1.0350000	1.0350000	1.5844032
2016	1.5511492	1.0350000	1.0350000	1.5308244
2017	1.4986949	1.0350000	1.0350000	1.4790574
2018	1.4480144	1.0350000	1.0350000	1.4290409
2019	1.3990477	1.0944308	1.0350000	1.3807159
2020	1.2783336	1.1000000	1.1000000	1.3340250
2021	1.1621214	1.0540784	1.1000000	1.2127500
2022	1.1025000	1.0500000	1.0500000	1.1025000
2023	1.0500000	1.0500000	1.0500000	1.0500000

[henrydingliu]

p = pd.DataFrame({'Year': list(range(2014,2025)), 'Premium': [10000]*11})
p_tri = cl.Triangle(p, origin='Year', columns='Premium', cumulative = True)

test = cl.Trend(
    trends=[.05, .1, .035],
    dates=[('2024-12-31', '2022-12-31'),('2022-12-31', '2019-12-31'),('2019-12-31','1990-1-1')]
).fit(p_tri).trend_.latest_diagonal.to_frame()
test['YoY'] = test['2024'] / test.shift(periods=-1)['2024']
test

this worked for me

[kennethshsu]

Wow I think you figured it out! Thank you!!!!

I think the next step is to let .Trend() estimate the trend, and move this to .TrendConstant(), similar to the development sister function. I think we should flip the dates though, so they have (start, end) pair.

[henrydingliu]

I'm looking through Friedland. Chapter 8 Expected Claims and Chapter 11 Freq-Sev both heavily mention applying trend but does not offer any guidance on how to select trend. I would posit that we don't need to implement a trend estimator before 1.0. If we have bandwidth, I actually think implementing apriori estimation into the expected loss IBNR method is a more core need. As a part of that apriori estimation, we'll have a chance to tweak the (end, start) tuple definition to be more aligned with the textbook.