Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2024-09-01
Price Estimation via Bayesian Filtering and Optimal Bid--Ask Prices for Market Makers
Hyungbin Park, Junsu ParkAbstract : This study estimates the true price of an asset and finds the optimal bid/ask prices for market makers. We provide a novel state-space model based on the exponential Ornstein--Uhlenbeck volatility and the Heston models with Gaussian noise, where the traded price and volume are available, but the true price is not observable. An objective of this study is to use Bayesian filtering to estimate the posterior distribution of the true price, given the traded price and volume. Because the posterior density is intractable, we employ the guided particle filtering algorithm, with which adaptive rejection metropolis sampling is used to generate samples from the density function of an unknown distribution. Given a simulated sample path, the posterior expectation of the true price outperforms the traded price in estimating the true price in terms of both the mean absolute error and root-mean-square error metrics. Another objective is to determine the optimal bid/ask prices for a market maker. The profit-and-loss of the market maker is the difference between the true price and its bid/ask prices multiplied by the traded volume or bid/ask size of the market maker. The market maker maximizes the expected utility of the PnL under the posterior distribution. We numerically calculate the optimal bid/ask prices using the Monte Carlo method, finding that its spread widens as the market maker becomes more risk-averse, and the bid/ask size and the level of uncertainty increase.
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2023-07-01
Complex reflection groups and K3 surfaces II. The groups ${\boldsymbol{G_{29}}}$, ${\boldsymbol{G_{30}}}$ and ${\boldsymbol{G_{31}}}$
Cédric Bonnafé, Alessandra SartiAbstract : We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W.~Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.
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2023-09-01
Almost universal sums of triangular numbers with one exception
Jangwon JuAbstract : For an arbitrary integer $x$, an integer of the form $T(x)\!=\!\frac{x^2+x}{2}$ is called a triangular number. Let $\alpha_1,\dots,\alpha_k$ be positive integers. A sum $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=\alpha_1 T(x_1)+\cdots+\alpha_k T(x_k)$ of triangular numbers is said to be {\it almost universal with one exception} if the Diophantine equation $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=n$ has an integer solution $(x_1,\dots,x_k)\in\mathbb{Z}^k$ for any nonnegative integer $n$ except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of ``15-theorem" of Conway, Miller, and Schneeberger.
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2023-01-01
Minimal polynomial dynamics on the $p$-adic integers
Sangtae JeongAbstract : In this paper, we present a method of characterizing minimal polynomials on the ring ${\mathbf Z}_p$ of $p$-adic integers in terms of their coefficients for an arbitrary prime $p$. We first revisit and provide alternative proofs of the known minimality criteria given by Larin [11] for $p=2$ and Durand and Paccaut [6] for $p=3$, and then we show that for any prime $p\geq 5,$ the proposed method enables us to classify all possible minimal polynomials on ${\mathbf Z}_p$ in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.
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2023-01-01
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben SeghierAbstract : Let $\alpha\in(0,\infty)$, $p\in(0,\infty)$ and $q(\cdot): {{\mathbb R}}^{n}\rightarrow[1,\infty)$ satisfy the globally log-H\"{o}lder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator $M$ and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley $g$-function and the Littlewood-Paley $g^{\ast}_{\lambda}$-function.
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2023-05-01
Temporal decay of solutions for a chemotaxis model of angiogenesis type
Jaewook Ahn, Myeonghyeon KimAbstract : This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in $\mathbb{R}^{d}$, $d\ge3$, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.
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2023-05-01
Schur convexity of $L$-conjugate means and its applications
Chun-Ru Fu
, Huan-Nan Shi, Dong-Sheng WangAbstract : In this paper, using the theory of majorization, we discuss the Schur $m$ power convexity for $L$-conjugate means of $n$ variables and the Schur convexity for weighted $L$-conjugate means of $n$ variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about $n$ variables Gini mean are established.
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2023-03-01
Ramanujan continued fractions of order eighteen
Yoon Kyung ParkAbstract : As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction $C(\tau)$. We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.
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2023-05-01
On relative Cohen-Macaulay modules
Zhongkui Liu, Pengju Ma, Xiaoyan YangAbstract : Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$. We give some descriptions of the $\mathfrak{a}$-depth of $\mathfrak{a}$-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaul-\\ayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.
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2024-03-01
Asymptotic behavior of solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays
Cung The Anh, Vu Manh Toi, Phan Thi TuyetAbstract : This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space $BCL_{-\infty}(H)$. We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.
Most Read
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Price Estimation via Bayesian Filtering and Optimal Bid--Ask Prices for Market Makers
Hyungbin Park, Junsu Park
J. Korean Math. Soc. 2024; 61(5): 875-898
https://doi.org/10.4134/JKMS.j230053 -
Complex reflection groups and K3 surfaces II. The groups ${\boldsymbol{G_{29}}}$, ${\boldsymbol{G_{30}}}$ and ${\boldsymbol{G_{31}}}$
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014 -
Almost universal sums of triangular numbers with one exception
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231 -
Minimal polynomial dynamics on the $p$-adic integers
Sangtae Jeong
J. Korean Math. Soc. 2023; 60(1): 1-32
https://doi.org/10.4134/JKMS.j210494
Most Downloaded
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Almost universal sums of triangular numbers with one exception
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231 -
Minimal polynomial dynamics on the $p$-adic integers
Sangtae Jeong
J. Korean Math. Soc. 2023; 60(1): 1-32
https://doi.org/10.4134/JKMS.j210494 -
Complex reflection groups and K3 surfaces II. The groups ${\boldsymbol{G_{29}}}$, ${\boldsymbol{G_{30}}}$ and ${\boldsymbol{G_{31}}}$
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014 -
Price Estimation via Bayesian Filtering and Optimal Bid--Ask Prices for Market Makers
Hyungbin Park, Junsu Park
J. Korean Math. Soc. 2024; 61(5): 875-898
https://doi.org/10.4134/JKMS.j230053
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