A Collective Investment Problem in a Stochastic Volatility Environment: The Impact of Sharing Rules

34 Pages Posted: 24 Jul 2019

See all articles by An Chen

An Chen

University of Ulm

Thai Nguyen

University of Ulm - Institute of Insurance Science

Manuel Rach

University of Ulm - Institute of Insurance Science

Date Written: July 23, 2019

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

JEL Classification: G11, G23

Suggested Citation

Chen, An and Nguyen, Thai and Rach, Manuel, A Collective Investment Problem in a Stochastic Volatility Environment: The Impact of Sharing Rules (July 23, 2019). Available at SSRN: https://ssrn.com/abstract=3424804 or http://dx.doi.org/10.2139/ssrn.3424804

An Chen

University of Ulm ( email )

Helmholtzstrasse 20
Ulm, D-89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Thai Nguyen

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

Manuel Rach (Contact Author)

University of Ulm - Institute of Insurance Science ( email )

Ulm, 89081
Germany

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