AMLCR (2nd edition) Sec. 7.3 p.189
Could someone check if I understand the book correctly and provide comments:
In example 7.3, Interest rate for premium calculation (e.g., i(p)=6%) > Interest rate for reserve calculation (e.g., i(r)=5%).
If the gross premium is calculated using equivalence principle and interest rates were the same (i(p)=i(r)), then V_0=0.
Now i(r)<i(p), and as a consequence V_0>0. V_t(i(r))>V_t(i(p)) for all t because the duration of future premiums < duration of future benefits for all t (as long as the policy is well designed).
The textbook refers to the reserve valuation assumption “i(r)<i(p)” as “policy value basis is more conservative (lower i) than premium basis (higher i)”. I wonder if it works this way in practice:
A more “conservative” reserve basis yield a “higher” reserve value. The insurer hence needs to allocate a higher reserve to allow for uncertainty or adverse experience. This way, the profit is released later than if one set i(r)=i(p).
Am I right?
Could someone check if I understand the book correctly and provide comments:
In example 7.3, Interest rate for premium calculation (e.g., i(p)=6%) > Interest rate for reserve calculation (e.g., i(r)=5%).
If the gross premium is calculated using equivalence principle and interest rates were the same (i(p)=i(r)), then V_0=0.
Now i(r)<i(p), and as a consequence V_0>0. V_t(i(r))>V_t(i(p)) for all t because the duration of future premiums < duration of future benefits for all t (as long as the policy is well designed).
The textbook refers to the reserve valuation assumption “i(r)<i(p)” as “policy value basis is more conservative (lower i) than premium basis (higher i)”. I wonder if it works this way in practice:
A more “conservative” reserve basis yield a “higher” reserve value. The insurer hence needs to allocate a higher reserve to allow for uncertainty or adverse experience. This way, the profit is released later than if one set i(r)=i(p).
Am I right?
AMLCR“policy value basis is more conservative (lower i)than premium basis (higher i)”
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