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The Impact of Medical CostInflation and Dynamic
Policyholder Behavior onMarket Consistent Embedded
Value in Health Insurance
Jan-Philipp SchmidtMarcus C. Christiansen
Session Number: TBR6Joint IACA, IAAHS and PBSS Colloquium in Hong Kong
www.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Motivation
I What is the shareholder value from long-term insurancecontracts?
I How do the inflation and medical inflation affect theshareholders value and risk associated with the value?
I How is the value affected by dynamic policyholder behavior?
Analysis based on stochastic insurance company model for Germanprivate health insurance companies (introduced in Schmidt(2012)).
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Framework
Stochastic Environment: External factors
(Ω,F ,P) prob. spaceX1, . . . ,Xn r.v.with Xi : Ω→ RT
1 ≤ i ≤ n
Insurance Company: Cash flows Y = f (X1, . . . ,Xn)
Valuation: Value e.g. E(g(Y ))
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Inflation and Medical Inflation in Germany
Analysis of data set from German supervisor (BaFin):
2002 2004 2006 2008 20100 %
2 %
4 %
6 %inflation rate
claim increase
2002 2004 2006 2008 20100 %
2 %
4 %
6 %spread
average spread (2002-2010)
Claim increase: Average annual increase of claim reimbursement (policyholders
aged 25-80) for outpatient benefits in all German private health insurance
tariffs. Inflation rate: Increase in Consumer Price Index CPI (Germany)
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Stochastic Environment
I Consider capital market model from Jarrow and Yildirim (2003)with risk factors nominal and real term structure and inflation.
I σn, σr , σI volatility of processes, an, ar mean reversion speedI (Wn,Wr ,WI ) Brownian motion for each risk factorI Correlations of Brownian motion ρn,r , ρn,I and ρr ,II ϑn(t), ϑr (t) functions to fit term structure of interest rates
I Medical inflation considered as an additive spread σ on top ofthe change in the inflation process.
I Analysis of impact of inflation and medical inflation by variationof . . .
I . . . medical inflation spread σI . . . volatility of inflation process I (t)
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Private Health Insurance in Germany
I Whole-life insurance guarantee
I Pricing and reserving similar to life insurance techniques(principle by equivalence, accumulation of actuarial reserve)
I Level premium at beginning of the contract linked toI genderI age at underwritingI risk classification at underwriting
I Insurance company renounces the right of contract cancellation
I Premium development over lifetime of a contract linked to claimand mortality experience in a tariff → Premium adjustment
I Safety loading factor of at least 5 % of premium
I Policyholders pay 10 % loading on premium until age 60 toaccumulate additional reserve for limiting premium increases incase of premium adjustments
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Premium Adjustments in German Private Health Insurance
I Annual check of first-order assumptionsI Claim reimbursementI Mortality rates
I Deviation between first-order assumptions and observationsabove threshold (at least 5 %) and deviation not temporarily:
I Check of all first-order assumptionsI If necessary: determination of new first-order assumptions
I Adjustment of first-order assumptions at the beginning of thefollowing year based on independent trustee agreement:
I Adjustment may result in new premiumI If premium increases: company performs limiting measures (profit
sharing)
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Impact of Inflation and Medical Inflation on Shareholder Profits
I Premium adjustment allows adjustment of first-orderassumptions and in particular adjustments of claim assumptions.
I Aggregation of different surpluses allows balancing of loss fromclaim development.
I Short-term effect: Inflation and medical inflationdisadvantageous for shareholders due to negative underwritingsurplus (until next premium adjustment).
I Long-term effect: Inflation and medical inflation in generaladvantageous for shareholders due to ‘increased’ insurancecoverage.
Which effect dominates?
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Dynamic Policyholder Behavior – Introduction
Policyholders’ propensity to exercise options in insurance contractsis influenced by external factors (Kent et al., 2009).
Options of policyholders in German health insurance, e.g.,
I lapse of contract and switch to other insurance company
I tariff switch or change of coverage (e.g. higher deductible)
Policyholder behavior may depend on several factors, e.g.
I age, gender and tariff of policyholder, . . .
I number of premium adjustments, development of premium, . . .
I contract duration, health status, sales channel, . . .
I development of capital market (e.g. term structure of interestrates), . . .
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Dynamic Policyholder Behavior – Lapse
I Policyholders: Lapse in general disadvantageous in financialterms due to (partial) loss of actuarial reserve.
I Shareholders: Lapse rates are part of first-order assumptions inpremium and reserve calculation. Impact of lapse is mainly basedon those first-order assumptions.
Short-term effect:
I Increase in actual lapse rates: Annual surplus increases
Long-term effect:
I Increase in actual lapse rates: Loss of future profits
Which effect dominates?
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Dynamic Policyholder Behavior – Modeling
Data set from German supervisor (BaFin) for male policyholders:
25 30 35 40 45 50 55 60 65 70 750 %
5 %
10 %
15 %
20 %
Age
lapse rates
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Dynamic Policyholder Behavior – Modeling
Based on previous 5 years the lapse rates from the previousslide are adjusted based on the following rule:
Check 1:Number of
adjustments?
Check 2: Premium increase?
decrease lapse rates by 1/(1 + `)
lowno change in lapse rates
high
≤2
Check 2:Premiumincrease?
no change in lapse rateslow
increase lapse rates by 1 + `
high
≥ 3
Check 2 compares the premium increase with the change ofinflation and medical inflation.
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Results – Medical Inflation (Spread)
0 % 1 % 2 % 3 % 4 % 5 %0 %
2 %
4 %
6 %
8 %
10 %
12 %
medical inflation spread
PVFP
MC
inre
lati
on
toa
sset
s
threshold 10 %
threshold 5 %
threshold 0 %
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Results – Medical Inflation (Volatility of Inflation)
0 % 1 % 2 % 3 % 4 % 5 %0 %
2 %
4 %
6 %
8 %
10 %
12 %
volatility of inflation process
PVFP
MC
inre
lati
on
toa
sset
s
threshold 10 %
threshold 5 %
threshold 0 %
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Results – Dynamic Policyholder Behavior
0 % 2 % 4 % 6 % 8 % 10 % 12 %0 %
2 %
4 %
6 %
8 %
10 %
12 %
parameter of lapse function `
PVFP
MC
inre
lati
on
toa
sset
s
threshold 10 %
threshold 5 %
threshold 0 %
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Agenda
Motivation
Stochastic Environment
Insurance Company
Dynamic Policyholder Behavior
Results
Conclusion and Outlook
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Conclusion and Outlook
I Inflation and medical inflation have a significant impact onshareholders value.
I Long-term effect dominates: A high medical inflation (spread ontop of CPI) may increase the shareholders value.
I Impact of inflation volatility is non-linear.
I Dynamic policyholder behavior affects shareholders value.I Long-term effect dominates: A higher policyholder sensitivity
decreases shareholders value slightly in our setting.I Policyholder behavior influenced by many more external and
internal factors.
I Further empirical studies necessary to determine the importanceof different factors on policyholder behavior in health insurance(work in progress).
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
Thank you very much for your attention.
Jan-Philipp Schmidt
University of UlmInstitute of Insurance Science89069 UlmGERMANY
jan-philipp.schmidt@uni-ulm.de
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
References
R. Jarrow and Y. Yildirim. Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJMModel. Journal of Financial and Quantitative Analysis, 38(2):337–358, 2003.
J. Kent, C. Legrand, and E. Morgan. Dynamic Policyholder Behaviour Survey. Presentationhttp://de.milliman.com/pdfs/dynamic-policy-behaviour-survey.pdf, 2009.
J.-P. Schmidt. Market-Consistent Valuation of Long-Term Insurance Contracts — Valuation Framework andApplication to German Private Health Insurance. http://www.uni-ulm.de, 2012.
Joint IACA, IAAHS and PBSS Colloquium in Hong Kongwww.actuaries.org/HongKong2012/
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