The Three-step method in a dynamic setting
(2025) , 33 pages
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- 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 Pure Endowment 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.
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Belhouari, O., Devolder, P., & Linders, D. (2025). The Three-step method in a dynamic setting (LIDAM Discussion Paper ISBA 2025/18).