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

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.

Retrospective Reserves and Bonus with Policyholder Behavior

“…In our model, we also consider dividends linked to the surplus, but, distinct from Steffensen (2006), we derive differential equations for the projected savings account and surplus. Jensen and Schomacker (2015) study the valuation of an insurance contract with the bonus scheme spoken of as additional benefits, where dividends are used to buy more insurance, in a scenario-based model for the financial market. Our paper has some similarities with Jensen and Schomacker (2015) in the sense that we also study a scenario-based model with additional benefits.…”

“…Jensen and Schomacker (2015) study the valuation of an insurance contract with the bonus scheme spoken of as additional benefits, where dividends are used to buy more insurance, in a scenario-based model for the financial market. Our paper has some similarities with Jensen and Schomacker (2015) in the sense that we also study a scenario-based model with additional benefits. In Jensen and Schomacker (2015), the bonus allocation is discretized, while we allocate bonus continuously, resulting in difference equations in Jensen and Schomacker (2015) and ordinary differential equations in our model.…”

“…Our paper has some similarities with Jensen and Schomacker (2015) in the sense that we also study a scenario-based model with additional benefits. In Jensen and Schomacker (2015), the bonus allocation is discretized, while we allocate bonus continuously, resulting in difference equations in Jensen and Schomacker (2015) and ordinary differential equations in our model. Furthermore, we study state-wise projections of the savings account and the surplus, whereas Jensen and Schomacker (2015) study the expected savings account and the expected surplus.…”

“…In Jensen and Schomacker (2015), the bonus allocation is discretized, while we allocate bonus continuously, resulting in difference equations in Jensen and Schomacker (2015) and ordinary differential equations in our model. Furthermore, we study state-wise projections of the savings account and the surplus, whereas Jensen and Schomacker (2015) study the expected savings account and the expected surplus. Steffensen (2006) considers prospective reserves, while we focus on the savings account, which is a retrospective reserve including past bonus, and the surplus of an insurance contract.…”

Technical reserves in insurance and Slovak insurance market

“…Published papers are addressing the topic at many circuits and partial questions. One factor that affects the calculation of technical provisions is an assessment of the risk, which is a very complex problem [3][4][5] Expedient are analysis, evaluation and reports on regional and national levels that explain the specifics of a particular insu rance sector [6][7][8][9][10]. The attention is paid at the application of mathematical and statistical methods and modelling in order to apply procedures that allow implementing processes which take into account all the elements for the calculation [10][11][12].…”