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AIMS Mathematics

2020, Volume 5, Issue 1: 300-310. doi: 10.3934/math.2020020
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Research article

Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling

  • 1.
    Department of Mathematical Sciences, Institute of Business Administration Karachi, Pakistan
  • 2.
    University of Bucharest, Romania
  • 3.
    "Gh. Mihoc-C. Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
  • 4.
    National Institute for Economic Research "Costin C. Kiritescu", Bucharest, Romania
  • 5.
    Bucharest University of Economic Studies, Bucharest, Romania
  • Received: 15 August 2019 Accepted: 04 November 2019 Published: 13 November 2019

  • MSC : 60Gxx, 60Jxx, 90Bxx

  • A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt & Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho & Lee model in the semi-Markov regime-switching framework [1]. We formulate and solve the optimization problem of Hunt & Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [2]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques.

    Citation: Muhammad Sheraz, Vasile Preda, Silvia Dedu. Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling[J]. AIMS Mathematics, 2020, 5(1): 300-310. doi: 10.3934/math.2020020

    Related Papers:

  • A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt & Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho & Lee model in the semi-Markov regime-switching framework [1]. We formulate and solve the optimization problem of Hunt & Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [2]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques.


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