On Smoothing and Habit Formation of Variable Life Annuity Benefits

Mogens Steffensen and Savannah Halling Vikkelsøe ()
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Mogens Steffensen: Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen Ø, Denmark
Savannah Halling Vikkelsøe: Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen Ø, Denmark

JRFM, 2024, vol. 17, issue 2, 1-27

Abstract: 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.

Keywords: optimal consumption and investment; consumption dynamics; smooth pension product; decumulation phase (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
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