Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation

TL;DR

This paper proposes a new valuation framework called two-step actuarial valuations that ensures actuarial risks are priced consistently with standard principles, linking it to market-consistent valuations and dependence structures.

Contribution

It introduces the concept of actuarial-consistent valuations and demonstrates their equivalence to two-step actuarial valuations under coherence, extending actuarial principles.

Findings

Actuarial-consistent valuations depend on both financial and actuarial risks.

Two-step actuarial valuations are equivalent to actuarial-consistent valuations under coherence.

Dependence between risks influences valuation outcomes.

Abstract

This paper introduces new valuation schemes called actuarial-consistent valuations for insurance liabilities which depend on both financial and actuarial risks, which imposes that all actuarial risks are priced via standard actuarial principles. We propose to extend standard actuarial principles by a new actuarial-consistent procedure, which we call "two-step actuarial valuations". \bluebis{In the case valuations are coherent}, we show that actuarial-consistent valuations are equivalent to two-step actuarial valuations. We also discuss the connection with "two-step market-consistent valuations" from Pelsser and Stadje (2014). In particular, we discuss how the dependence structure between actuarial and financial risks impacts both actuarial-consistent and market-consistent valuations.