Optimal Capital Structure for Life Insurance Companies Offering Surplus Participation

TL;DR

The paper extends Leland's dynamic capital-structure framework to life insurers offering surplus participation by modeling the surplus as a barrier-option payoff paid only if solvency holds. It derives the endogenous bankruptcy-triggering value $V_B$, and then obtains conditions and equations for the optimal participation rate $\alpha^*$ and guarantee rate $g^*$, including joint optimization. The main findings show that tax benefits strongly influence the attractiveness of surplus participation and that incorporating surplus participation reduces asset-substitution incentives for reasonable contract durations. The results offer a mechanistic, capital-structure-based rationale for the prevalence of participating life-insurance contracts and related hybrid products in practice, with implications for product design and regulation.

Abstract

We adapt Leland's dynamic capital structure model to the context of an insurance company selling participating life insurance contracts explaining the existence of life insurance contracts which provide both a guaranteed payment and surplus participation to the policyholders. Our derivation of the optimal participation rate reveals its pronounced sensitivity to the contract duration and the associated tax rate. Moreover, the asset substitution effect, which describes the tendency of equity holders to increase the riskiness of a company's investment decisions, decreases when adding surplus participation.

Figures (9)

• Figure 1: Market share in 2022 of the gross premium separated by the line of business in the life sector. Data source: European Insurance Overview from the EIOPA EIOPAreport
• Figure 2: Plot of the right hand side of \ref{['eq: formula for vb']} (left) and of its first line and the negative of its second line (right). Note that the intersection with $0$ (left) resp. of the two lines (right) is $V_B$.
• Figure 3: Equity value as a function of the asset value with an $\alpha$ such that $V \to E(V)$ is non-decreasing (left) and if it does not hold (right). In both plots is $V_B$ chosen for the left case.
• Figure 4: Scatterplot if the optimal rates are positive as functions of the liability ratio $\frac{P}{V_0}$ (in %) and the tax benefit $\tau=\tau_1=\tau_2$ (left) resp. the guarantee rate $\frac{G}{P}$ (in %) (right). A white square indicates that $\alpha^*>0$ in the left and the right plot resp. that $g^*>0$ holds in the middle plot.
• Figure 5: Variation of the bankruptcy-triggering value $V_B$ for different values of the participation rate $\alpha$ (with $\alpha<\bar{\alpha}$) and the guaranteed payment rate $\frac{G}{P}$.

Theorems & Definitions (41)

• Theorem 3.1
• Proposition 3.2
• Proposition 3.3
• Proposition 3.4
• Corollary 3.5
• Corollary 3.6
• Proposition 4.1
• Theorem 4.2
• Proposition 4.3
• Theorem 4.4