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Mandatory disclosure in oligopolistic market making

2026-05-31T15:00:00Z

Title: Mandatory disclosure in oligopolistic market making Author(s): Kim, Seongjin; Choi, Jin Hyuk Abstract: We develop a multi-period Kyle-type model that incorporates both mandatory disclosure of informed trades and imperfect competition among market makers. We prove the existence and uniqueness of a linear equilibrium and show that the liquidity-enhancing effect of disclosure is fundamentally linked to the degree of market-making competition. Disclosure lowers trading costs by reducing price impact, and its marginal benefit is strictly larger when competition is weak. We empirically validate this prediction using the 2002 Sarbanes-Oxley Act disclosure reform as a natural experiment. A difference-in-differences analysis of U.S. equities confirms that the spread reduction following enhanced disclosure is significantly larger for stocks with fewer active market makers.

GLOBAL REGULARITY FOR SOME AXISYMMETRIC EULER FLOWS IN Rd

2025-12-31T15:00:00Z

Title: GLOBAL REGULARITY FOR SOME AXISYMMETRIC EULER FLOWS IN Rd Author(s): Choi, Kyudong; Jeong, In-Jee; Lim, Deokwoo Abstract: We consider axisymmetric Euler flows without swirl in Rd with d >= 4, for which the global regularity of smooth solutions is an open problem. When d = 4, we obtain global regularity under the assumption that the initial vorticity satisfies some decay at infinity and is vanishing at the axis. Assuming further that the initial vorticity is of one sign guarantees global regularity for d <= 7.

Some applications of the traces of Frobenius of elliptic curves in a certain family

2026-07-31T15:00:00Z

Title: Some applications of the traces of Frobenius of elliptic curves in a certain family Author(s): Cho, Peter J.; Yoo, Jinjoo Abstract: Let J = {a, b} be an unordered pair of elements of Fq and EJ the associated elliptic curve of the form y 3 = (x − a)(x − b) over Fq. Using its trace of Frobenius, we obtain several applications. We first compute the average analytic rank of elliptic curves for our family and generate elliptic curves with designated extremal primes. Furthermore, we determine explicit and average values on class numbers of every constant field extension of KJ := Fq(T, p3 (T − a)(T − b)). Finally, we estimate the exact values and average values on Euler-Kronecker constants of KJ .

Existence and Stability of Sadovskii Vortex Patch: an odd-symmetric touching pair of uniform vortices

2026-01-31T15:00:00Z

Title: Existence and Stability of Sadovskii Vortex Patch: an odd-symmetric touching pair of uniform vortices Author(s): Sim, Young-Jin Abstract: As a traveling solution of the two-dimensional incompressible Euler equations, the Sadovskii vortex patch takes the form of a counter-rotating pair of vortex patches that are in contact. This model was suggested by Sadovskii [J. Appl. Math. Mech., 1971] and has since attracted considerable attention due to its significance to the inviscid limit of planar flows via the Prandtl–Batchelor theory and its role as an asymptotic state of the dynamics of vortex rings. In this paper, we establish the existence and stability of the Sadovskii vortex patch. First, we show that a Sadovskii vortex patch arises as a maximizer of the kinetic energy under an exact impulse condition. By analyzing the fluid velocity along the symmetry axis and its relation to the vorticity of a dipole, we verify that two patches in the dipole are in contact. Second, we construct a subcollection of such energy maximizers that is stable in the following sense: if an initial vorticity is sufficiently close to a maximizer, then the corresponding solution remains close to this collection up to a translation and travels at a similar speed to the maximizers. This is achieved via a concentration–compactness argument together with the conservation of impulse, circulation, and kinetic energy in time. Furthermore, using uniform estimates of energy maximizers and a shift estimate obtained by estimating the center of mass of the solution, we show that the solution keeps its touching structure uniformly in time. Major: Department of Mathematical Sciences