Mongolian Mathematical Journal 2023-10-09T01:48:11+00:00 L.Altangerel Open Journal Systems <p>Mongolian Mathematical Journal (MMJ) was originally founded in 1997 by the Mongolian Mathematical Society with the financial support of the National University of Mongolia (1997-2003 named “Journal of Mongolian Mathematical Society”).</p> <p>MMJ is a peer-reviewed journal for the publication of original and survey papers in pure and applied mathematics</p> Rainbow Options with MS–VAR process 2023-10-09T01:38:35+00:00 Battulga Gankhuu <p>This paper presents pricing and hedging methods for rainbow options and lookback options under Markov-Switching Vector Autoregressive (MS–VAR) process. Here we assumed that a regime–switching process is generated by a homogeneous Markov<br>process. An advantage of our model is it depends on economic variables and simple as compared with previous existing papers.</p> 2023-08-31T00:00:00+00:00 Copyright (c) 2022 Battulga Gankhuu Optimal Control Sphere Packing Problem 2023-10-09T01:42:08+00:00 Rentsen Enkhbat <p>The sphere packing problem which is to pack non-overlapping spheres with the maximum volume into a convex set. The problem belongs to a class of global optimization. Convex maximization formulation of the problem is given in [1, 12]. In this paper, we formulate a new optimal control problem based on the sphere packing problem which is a nonconvex optimal control problem with phase and control constraints. A discrete version of the new optimal control problem for sphere packing problem has been<br>discussed. We examine also Malfatti’s problem [17] from a view point of optimal control theory.</p> 2023-08-31T00:00:00+00:00 Copyright (c) 2022 Rentsen Enkhbat Applications of Fenchel Duality for Vector Optimization Problems 2023-10-09T01:45:13+00:00 Lkhamsuren Altangerel <p>This paper deals with applications of Fenchel duality for vector optimization problems based on alternative definitions of the conjugate maps and the subgradient for a set-valued map having vector variables (cf. [3]). Some results investigated in Section 4 in [3] allow us to consider applications presented in this paper.</p> 2023-08-31T00:00:00+00:00 Copyright (c) 2023 Lkhamsuren Altangerel Boundedness of Some Hilbert–Type Operators on the Weighted Morrey–Herz Spaces 2023-10-09T01:48:11+00:00 Tserendorj Batbold Amarsaikhan Amarbayar Mario Krni´c <p>In this paper we establish necessary and sufficient conditions for the boundedness of a general Hilbert-type operator on the weighted Morrey-Herz spaces, without imposing conditions on a homogeneous kernel. As an application, some particular cases are also considered. Our results are compared with some previously known from the literature.</p> 2023-08-31T00:00:00+00:00 Copyright (c) 2023 Tserendorj Batbold, Amarsaikhan Amarbayar, Mario Krni´c