A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk

Ninna Reitzel Jensen and Kristian Juul Schomacker
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Ninna Reitzel Jensen: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark
Kristian Juul Schomacker: Edlund A/S, Bjerregårds Sidevej 4, DK-2500 Valby, Denmark

Risks, 2015, vol. 3, issue 2, 1-36

Abstract: Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events, such as death, disability, etc. In our treatment of participating life insurance, we have special focus on the bonus schemes “consolidation” and “additional benefits”, and one goal is to formalize how these work and interact. Another goal is to describe similarities and differences between participating life insurance and unit-linked insurance. By use of a two-account model, we are able to illustrate general concepts without making the model too abstract. To allow for complicated financial markets without dramatically increasing the mathematical complexity, we focus on economic scenarios. We illustrate the use of our model by conducting scenario analysis based on Monte Carlo simulation, but the model applies to scenarios in general and to worst-case and best-estimate scenarios in particular. In addition to easy computations, our model offers a common framework for the valuation of life insurance payments across product types. This enables comparison of participating life insurance products and unit-linked insurance products, thus building a bridge between the two different ways of formalizing life insurance products. Finally, our model distinguishes itself from the existing literature by taking into account the Markov model for the state of the policyholder and, hereby, facilitating event risk.

Keywords: two-account model; economic scenarios; participating life insurance; unit-linked insurance; stochastic differential equations; guarantees; bonus; fairness; market valuation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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