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Optimal Portfolio Selection for an Investor with Asymmetric Attitude to Gains and Losses

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Sergei Sidorov

    (Saratov State University)

  • Andrew Khomchenko

    (Saratov State University)

  • Sergei Mironov

    (Saratov State University)

Abstract

The description of Cumulative Prospect Theory (CPT) includes three important parts: a value function over outcomes, v(⋅ ); a weighting function over cumulative probabilities, w(⋅ ); CPT-utility as unconditional expectation of the value function v under probability distortion w. In this paper we consider the problem of choosing an CPT-investor’s portfolio in the case of complete market. The problem of finding the optimal portfolio for CPT-investor is to maximize the unconditional expectation of the value function v under probability distortion w over terminal consumption, subject to budget constraint on initial wealth. We find the optimal payoffs for CPT-investor for the classic Black-Scholes environment assuming that there are a single lognormally distributed stock and a risk free bond. We compare the optimal payoffs of CPT-investor with the optimal payoffs of the investor that maximizes expected power utility over terminal payoffs, subject to budget constraint on initial wealth.

Suggested Citation

  • Sergei Sidorov & Andrew Khomchenko & Sergei Mironov, 2017. "Optimal Portfolio Selection for an Investor with Asymmetric Attitude to Gains and Losses," Springer Books, in: Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 157-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50234-2_13
    DOI: 10.1007/978-3-319-50234-2_13
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