The next step in performance monitoring – Stochastic monitoring (and reserving!)

The next step in performance monitoring – Stochastic monitoring(and reserving!) NZ Actuarial Conference November 2010

Agenda • Monitoring of claim experience • Adding some confidence • Stochastic reserving • Questions…

What is monitoring? • Wikipedia definition: • The act of listening, carrying out surveillance on, and/or • The act of detecting the presence of signals • Actuarial interpretation: • To identify when experience is contrary to expected such that appropriate action can be taken when required.

Case study • Consider a Workers’ Compensation portfolio with periodic income benefits • Focus on the model of payments per active claim • Initial model established at December 2008 and monitored quarterly until March 2010

Case study – basic monitoring • Actual has increased rapidly at Dec 09 and Mar 10, but is it significant or simply random variation?

Tabulated results Detailed results Case study – basic monitoring

Case study – initial model Chart shows average of the last 4 payment quarters compared to the selected December 2008 model

Case study – basic monitoring • Is this volatility unusual? Is a change in assumption indicated?

Case study – 5 quarters on Significant? Chart shows average of the 5 payment quarters to Mar 2010 compared to the selected December 2008 model

Case study – combined Was it ever significant?

Case study Difficult to determine “real change” vs random variation Often reliant on valuation actuary’s “judgment” in how best to respond Impact of judgement is not assessable at the time, and Generally not subject to hindsight review

Step 1 – use all the data Stochastic approach Traditional approach Development quarter Development quarter Accident quarter Accident quarter Data used to set assumptions Data used to set assumptions

Step 1 – use all the data • Note • The relative smoothness and sensible shape of the curve, and • The variability of an individual development quarter even using all the data!

Step 2 – break development curve into sections • Each section is controlled by a single parameter allowing it to move up or down over time

Step 3 – plot the history of each section over time and project • The early part of the development curve has moved up and down over time • The projection of these payment parameters completely determines the valuation Projection Strong SI

Step 4 – monitor parameter experience until the next valuation • By 2nd quarter there is a statistically significant difference between the projection and experience. Clear evidence for assumption change Inter-valuation experience Projection Strong SI

Another eg – development quarters 20 plus • Each section is controlled by a single parameter allowing it to move up or down over time

Step 3 – again, plot the history of each section over time and project • Slight upward trend in fitted curve indicates 0.6% p.a. SI consistent across time • Typically this would be missed by non-stochastic valn methods Projection Slight SI

Step 4 – monitor parameter experience until the next valuation • Combined, the last two quarters show that there is a statistically significant difference between the projection and experience. Inter-valuation experience Projection Slight SI

Step 4 – last 2 quarters combined Fitted falls outside the confidence interval • Having combined last 2 estimates, giving a narrower confidence interval we see that the fit clearly falls outside the 95% CI • Ie, a 5% level of significance hypothesis test concludes that the experience has altered

Why use stochastic (GLM) reserving models? • Allows stochastic monitoring to be carried out • ...which improves understanding of underlying trends • ...and gives earlier warning of changes • More likely to produce more accurate valuations • ...less prone to bias • ...able to find underlying trends not readily observable by the human eye • It’s easier and faster (except the first time)!

Dealing with some common misconceptions • Fantasy • Time consuming • Black box and difficult to understand • The results are not transparent • Can’t apply judgement • Reality • Like all modelling significant upfront establishment required. Once established more efficient than traditional methods • Output provides additional insights • Professional judgement remains a key feature • Stochastic reserving follows exactly the same path with the same input and output as traditional models • Help is available! • Don’t have to licence additional software to do it (most organisations have sas)

Reserving

Reserving Vol weighted averages recent diagonals e.g. Excel spreadsheet Traditional e.g. Excel spreadsheet e.g. Excel spreadsheet e.g. Excel spreadsheet

Reserving e.g. Excel to SAS, convert to columns e.g. Excel spreadsheet Vol weighted averages recent diagonals e.g. Excel spreadsheet Traditional e.g. Excel spreadsheet e.g. Excel spreadsheet e.g. Excel spreadsheet Stochastic Fit GLM using SAS or other statistical software e.g. SAS output to Excel e.g. Excel spreadsheet

First time GLM fitting procedure • Identify model structure • Fit saturated model • Simplify development curve shape • Simplify payment or accident year trends • Add seasonal patterns • Search for interactions • Review output and fit diagnostics • Triangles of fitted values and comparison of actual v fitted • AvE summaries by development period, payment period and accident period

Simplify development curve shape

Some standard diagnostics

Second and subsequent valuations • Run previous model on updated data set • Review diagnostics on updated model • Adjust model when necessary

Back to the case study...Conventional view of GLM fit vs 4 qtr avg

Conventional view of GLM fit vs 4 qtr avg plus traditional model fit

Conventional view of GLM fit vs 4 qtr avg plus traditional model fit Traditional methodology has underestimated the trends

Conventional view of GLM fit vs 4 qtr avg plus traditional model fit The traditional fit under-estimated the tail by about 5% (excl SI)

Key points • Stochastic monitoring enables the user to readily determine changes in experience • Earlier warning than traditional model • Identify when response required • Stochastic models for reserving readily identify trends over the entire triangle of experience • Less prone to bias • Better able to capture underlying trends in experience • Ability to analyse the data by numerous variables to check the model fit

The next step in performance monitoring – Stochastic monitoring (and reserving!)