The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies

Abstract

Traditional life insurance policies in many markets are sold with minimum interest rate guarantees. This paper concentrates on the risk cliquet-style guarantees impose on the insurer, measured by shortfall probabilities under the so-called "real-world probability measure P". We develop a general model and analyze the impact of interest rate guarantees on the risk of an insurance company. Furthermore the paper is concerned with how default risk depends on characteristics of the contract, on the insurer's reserve situation and asset allocation, and on management decisions as well as on regulatory parameters. In particular, the interaction of the parameters is analyzed yielding results that should be of interest for insurers as well as regulators.

A general asset–liability management model for the efficient simulation of portfolios of life insurance policies

“…Similar as the bonus reserve in [15], Q k is a hybrid determined as the difference between a market value C k and three book values D k , B k and F k . It may be interpreted as hidden reserve of the company as discussed in [22]. Similar balance sheets have already been considered in the literature.…”

“…Similar balance sheets have already been considered in the literature. The sum M k = D k + B k corresponds, e.g., to the policy reserve in [15], the policyholders' account in [22] or to the customer account in [24]. We prefer to separate the two accounts in order to thoroughly distinguish the effects of the bonus distribution from the guaranteed benefits.…”

“…This task can be achieved by performing stochastic simulations of ALM models in a risk-neutral environment. Much effort has been spent on the development of such models in the last years, see, e.g., [1,2,8,11,14,15,16,22,24,27] and the references therein. Thereby, most authors focus on the fair valuation and contract design of unit-linked and participating life insurance policies.…”

“…Thereby, most authors focus on the fair valuation and contract design of unit-linked and participating life insurance policies. Exceptions are [14,22] where the financial risks and returns of participating policies are analysed under the real world probability measure. Most of the existing literature (exceptions are [2,3,11]) restrict themselves to single-premium contracts and neglect mortality to simplify the presentation or to obtain analytical solutions.…”

Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment

“…Only if the reserves dropped beneath or rose above certain levels would the companies reduce or increase the surplus, respectively. The following distribution rule originally introduced by Kling et al (2004) was designed to model this behavior.…”