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Cooperative investment in incomplete markets under financial fairness

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  • Pazdera, Jaroslav
  • Schumacher, Johannes M.
  • Werker, Bas J.M.

Abstract

Groups of agents, such as participants in a collective pension fund, can decide to undertake a joint investment and to define, ex ante, a rule for the division of proceeds. The collective investment decision and the allocation rule together form a risk sharing scheme. Such a scheme defines a contingent claim for each participant. Given a proposed risk sharing scheme and an agreed-upon pricing functional, the values of these claims can be determined and can be compared to the values of the contributions made by the agents. A risk sharing scheme is said to be financially fair if, for each agent, the value of the agent’s claim as defined by the scheme is equal to the value of the agent’s contribution. The paper provides conditions under which there exists a unique risk sharing scheme that is both Pareto efficient (in the sense of expected utility) and financially fair. Furthermore, an iterative algorithm is presented by which this scheme can be computed. The theory is illustrated by a simple example which shows that, in an incomplete financial market, agents may benefit substantially from forming a collective.

Suggested Citation

  • Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:394-406
    DOI: 10.1016/j.insmatheco.2016.10.008
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    References listed on IDEAS

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    Cited by:

    1. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
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    3. Nicole Branger & An Chen & Antje Mahayni & Thai Nguyen, 2023. "Optimal collective investment: an analysis of individual welfare," Mathematics and Financial Economics, Springer, volume 17, number 5, June.
    4. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    5. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    6. Sander Muns & Bas J. M. Werker, 2022. "Pareto Optimal Pension Risk Allocations," De Economist, Springer, vol. 170(1), pages 133-172, February.
    7. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2017. "The composite iteration algorithm for finding efficient and financially fair risk-sharing rules," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 122-133.

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