TY - JOUR

T1 - On Smoothing and Habit Formation of Variable Life Annuity Benefits

AU - Steffensen, Mogens

AU - Vikkelsøe, Savannah Halling

N1 - Publisher Copyright: © 2024 by the authors.

PY - 2024

Y1 - 2024

N2 - This paper studies optimal consumption and investment strategies with lifetime uncertainty to design a smooth pension product. In a simplified Black–Scholes market, we investigate three strategies for consumption and investment: the classical strategy, the habit strategy, and the hybrid strategy. Incorporating additive habit formation in preferences leads to a request for less consumption volatility. Studying the consumption dynamics, it turns out that the hybrid strategy complies with the same preferences as the habit strategy. In our design of a smooth pension product, we are highly inspired by the consumption structure under the hybrid strategy and let consumption be specified as a time-dependent weighted average of last year’s consumption level and a standard market rate life annuity. We give two approaches for the investment portfolio. The numerical examples show that consumption under these approaches is less volatile than consumption under the classical strategy.

AB - This paper studies optimal consumption and investment strategies with lifetime uncertainty to design a smooth pension product. In a simplified Black–Scholes market, we investigate three strategies for consumption and investment: the classical strategy, the habit strategy, and the hybrid strategy. Incorporating additive habit formation in preferences leads to a request for less consumption volatility. Studying the consumption dynamics, it turns out that the hybrid strategy complies with the same preferences as the habit strategy. In our design of a smooth pension product, we are highly inspired by the consumption structure under the hybrid strategy and let consumption be specified as a time-dependent weighted average of last year’s consumption level and a standard market rate life annuity. We give two approaches for the investment portfolio. The numerical examples show that consumption under these approaches is less volatile than consumption under the classical strategy.

KW - consumption dynamics

KW - decumulation phase

KW - optimal consumption and investment

KW - smooth pension product

U2 - 10.3390/jrfm17020075

DO - 10.3390/jrfm17020075

M3 - Journal article

AN - SCOPUS:85187272875

VL - 17

JO - Journal of Risk and Financial Management

JF - Journal of Risk and Financial Management

SN - 1911-8066

IS - 2

M1 - 75

ER -