AIMS Mathematics, 2020, 5(1): 300-310. doi: 10.3934/math.2020020

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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

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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