A collective investment problem in a stochastic volatility environment: The impact of sharing rules

An Chen (), Thai Nguyen () and Manuel Rach ()
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An Chen: Institute of Insurance Science, Ulm University
Thai Nguyen: École d’Actuariat, Université Laval
Manuel Rach: Institute of Insurance Science, Ulm University

Annals of Operations Research, 2021, vol. 302, issue 1, No 4, 85-109

Abstract: Abstract It is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors’ well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

Keywords: Collective investment problems; Stochastic volatility; portfolio insurance; Sharing rules (search for similar items in EconPapers)
JEL-codes: G11 G23 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10479-021-03983-8

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