The Three-step method in a dynamic setting

Oussama Belhouari (), Pierre Devolder and Daniel Linders
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Oussama Belhouari: Université catholique de Louvain, LIDAM/ISBA, Belgium
Pierre Devolder: Université catholique de Louvain, LIDAM/ISBA, Belgium
Daniel Linders: University of Amsterdam

No 2025018, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: A crucial issue in a dynamic framework, is how risk valuations at different times are interrelated. In this regard, the notion of time consistency was widely introduced and discussed in the literature. A time-consistent dynamic valuation is a pricing method according to which a product that will be, in almost all states of nature, cheaper than another one at a future date should already be cheaper today. This paper aims to construct a time-consistent, dynamic version of the Three-step method introduced in [Deelstra et al., 2020] for hybrid life Pure Endowment products, employing a backward iteration scheme. The backward scheme is illustrated in a dual-iteration approach using a Pure Endowment product without profit sharing. Furthermore, we explore the continuous-time limit of the backward scheme, incorporating profit-sharing into the PureEndowment to investigate a hybrid life payoff. Our analysis demonstrates that the presence of the diversifiable component undermines the time-consistency of the dynamic Three-step method. Consequently, the time-consistent price of the actuarial part shows a notable increase. To address this, and in accordance with [Devolder and Leb`egue, 2016], we present a reduced time-consistent variant by decreasing the safety loads in each iterative step of the backward scheme.

Keywords: Premium principles; time-consistent; fair dynamic valuation; backward iteration scheme; hybrid life payoff (search for similar items in EconPapers)
Pages: 33
Date: 2025-10-29
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