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Black-Litterman model with intuitionistic fuzzy posterior return

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  • Krzysztof Echaust
  • Krzysztof Piasecki

Abstract

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On the side, intensive discussion shows that the experts' views are under knightian uncertainty. For this reason, we propose such variant of the Black - Litterman model in which the experts' views are described as intuitionistic fuzzy number. The existence of posterior return is proved for this case.We show that then posterior return is an intuitionistic fuzzy probabilistic set.

Suggested Citation

  • Krzysztof Echaust & Krzysztof Piasecki, 2016. "Black-Litterman model with intuitionistic fuzzy posterior return," Papers 1601.00354, arXiv.org.
    • Handle: RePEc:arx:papers:1601.00354
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Krzysztof Piasecki, 2013. "Behavioural present value," Papers 1302.0539, arXiv.org.
    3. Sharpe, William F., 1974. "Imputing Expected Security Returns from Portfolio Composition," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 463-472, June.
    4. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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