Mongolian Mathematical Journal

Rainbow Options with MS–VAR process

Battulga Gankhuu — 2023-08-31

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
process. An advantage of our model is it depends on economic variables and simple as compared with previous existing papers.

Optimal Control Sphere Packing Problem

Rentsen Enkhbat — 2023-08-31

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
discussed. We examine also Malfatti’s problem [17] from a view point of optimal control theory.

Applications of Fenchel Duality for Vector Optimization Problems

Lkhamsuren Altangerel — 2023-08-31

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.

Boundedness of Some Hilbert–Type Operators on the Weighted Morrey–Herz Spaces

Tserendorj Batbold — 2023-08-31

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.