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Mathematical model of European option pricing in incomplete market without transaction costs (discrete time ). Part I
Наноструктуры. Математическая физика и моделирование. 2020. Vol. 20. No. 1. P. 5–45.
For European option in multidimensional incomplete market without transaction costs we design discreet time pricing model. At first the following auxiliary problem is to be considered: to find the upper guaranteed value for the expected risk depending exponentialy on a shortage. The upper guaranteed value is a minimax of the expected risk. First we take supremum over a set of equivalent probability measures. Then we take infimum over a set of self-financing portfolios. Here we find conditions for the existence of a portfolio such that an infimum is attained. We use this result to find a generalized optional decomposition for a contingent claim. Further, we obtain conditions for the existence of a probability measure such that the expected risk is maximal with respect to the measure. This measure turned out to be martingale and discreet and it does not belong to the set of equivalent measures. Finally, we demonstrate that our auxiliary results make it possible to obtain explicit pricing formulas for an European option in an incomplete market without transaction costs. In part II of the paper we present example models of European options’ pricing in a one-dimensional market and in a market, where support of basic probability measure is compact.
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...
Added: December 1, 2025
Deviatov R., Baek S., / Series arXiv "math". 2025.
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...
Added: December 1, 2025
Nuriiat Omarovna Omarova, , in: The Youth in Science: Challenges and Prospects.: [б.и.], 2024. P. 64–72.
Hedges, expressions of doubt used in writing to tone down claims, are crucial in academic discourse, as they weaken assertions and make texts less categorical. Even though hedging in academic writing has attracted scholars’ attention, the number of works focusing on disciplinary variation in the use of hedges in L2 learners’ texts remains relatively scarce. ...
Added: October 30, 2024
Klementiev A., Вестник Пермского университета. Юридические науки 2024 № 3(65) С. 419–447
Introduction: there is no unity of approach to the concept of ‘derivative’ as a legal category in doctrine and in legislation. When defining the term ‘derivative financial instrument’, economists and financial experts base their definitions on the non-legal attribute of price derivativeness as well as on maturity of the assets. Purpose: to analyze approaches to ...
Added: October 2, 2024
Abul Hasan M., Asia and Africa today 2024 No. 4 P. 39–46
Abstract. The principle of non-alignment has been a cornerstone of Bangladesh’s foreign policy since its inception, holding significant relevance within both regional and global political contexts. But over time, local and external factors have caused the nation to stray from its founding ideals.
The author attempts to explore Bangladesh’s foreign relations choices, examining its historical context and ...
Added: May 3, 2024
Dikarev A., Lukin A., Pacific Review 2022 Vol. 35 No. 4 P. 617–646
The territorial dispute in the South China Sea (SCS) affecting China and several ASEAN countries has already resulted in drawn-out political tensions in the region. However, one aspect of the dispute is rarely discussed: its influence on Sino-Russian relations and its possible role as a case study in analysing the character of these relations. While ...
Added: June 27, 2022
Асмолов К. В., Soloviev A., Международная аналитика 2021 Т. 12 № 2 С. 49–73
The discourse of "strategic autonomy," going rounds in the Republic of Korea in recent years, has yet to undergo deep theoretical conceptualization. This article attempts to fill this gap by examining the South Korean discourse of "middlepowermanship", which sprouted the discourse of "strategic autonomy"; besides, the authors undertake socio-historical analysis of Korean perceptions of concept of ...
Added: January 27, 2022
Selivanovskiy A., Закон 2021 № 10 С. 51–81
In most OTC derivatives contracts, there is a power imbalance between the parties: the financial institution (the strongest party) has the expertise and experience in futures transactions and submits the contract documentation, while its client (the weakest party) often has no relevant experience and is confronted with such financial instruments for the first time. In ...
Added: November 11, 2021
Denisov I., Lukin A., Russian Politics 2021 Vol. 6 No. 4 P. 531–550
This article examines the state and prospects of Russia’s policy toward China. We look at recent trends in the evolution of the world order, the history of Moscow-Beijing relations, and the changes in the balance of power between Russia and China to offer a forecast of Russia’s China policy in the near term. Special attention ...
Added: November 2, 2021