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

Barigou, Karim; Linders, Daniël; Yang, Fan

doi:10.1080/03461238.2022.2090272

Cited by 4 publications

(1 citation statement)

References 37 publications

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“…Our work with the QP‐rule and the BEL approach can be seen as an application of the “two‐step market evaluation” in Pelsser and Stadje (2014) in the sense that first we start by conditioning with respect to financial events (see also Barigou et al., 2023). Second, we use the two same integrations with respect to conditioning and to risk neutral probability, as far as the integrand is a linear form of the contract.…”

Section: Introductionmentioning

confidence: 99%

Insurance–finance arbitrage

Artzner

Eisele

Schmidt

2023

Mathematical Finance

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Most insurance contracts are inherently linked to financial markets, be it via interest rates, or—as hybrid products like equity‐linked life insurance and variable annuities—directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furthermore, the insurer uses private information on top of the publicly available one about financial markets. This paper provides a study of the consistency of insurance contracts in connection with trades in the financial market with explicit mention of the information involved.By defining strategies on an insurance portfolio and combining them with financial trading strategies, we arrive at the notion of insurance–finance arbitrage (IFA). In analogy to the classical fundamental theorem of asset pricing, we give a fundamental theorem on the absence of IFA, leading to the existence of an insurance–finance‐consistent probability. In addition, we study when this probability gives the expected discounted cash‐flows required by the EIOPA best estimate.The generality of our approach allows to incorporate many important aspects, like mortality risk or general levels of dependence between mortality and stock markets. Utilizing the theory of enlargements of filtrations, we construct a tractable framework for insurance–finance consistent valuation.

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Section: Introductionmentioning

confidence: 99%

Insurance–finance arbitrage

Artzner

Eisele

Schmidt

2023

Mathematical Finance

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Robust asymptotic insurance-finance arbitrage

Oberpriller,

Ritter,

Schmidt

2024

Eur. Actuar. J.

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This paper studies the valuation of insurance contracts linked to financial markets, for example through interest rates or in equity-linked insurance products. We build upon the concept of insurance-finance arbitrage as introduced by Artzner et al. (Math Financ, 2024), extending their work by incorporating model uncertainty. This is achieved by introducing statistical uncertainty in the underlying dynamics to be represented by a set of priors $${{\mathscr {P}}}$$ P . Within this framework we propose the notion of robust asymptotic insurance-finance arbitrage (RIFA) and characterize the absence of such strategies in terms of the new concept of $${Q}{{\mathscr {P}}}$$ Q P -evaluations. This nonlinear two-step evaluation ensures absence of RIFA. Moreover, it dominates all two-step evaluations, as long as we agree on the set of priors $${{\mathscr {P}}}$$ P . Our analysis highlights the role of $${Q}{{\mathscr {P}}}$$ Q P -evaluations in terms of showing that all two-step evaluations are free of RIFA. Furthermore, we introduce a doubly stochastic model to address uncertainty for surrender and survival, utilizing copulas to define conditional dependence. This setting illustrates how the $${Q}{{\mathscr {P}}}$$ Q P -evaluation can be applied for the pricing of hybrid insurance products, highlighting the flexibility and potential of the proposed approach.

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