Hyeong-Ohk Bae | Ajou University South Korea (original) (raw)

Papers by Hyeong-Ohk Bae

Computational economics, Feb 17, 2024

arXiv (Cornell University), Oct 9, 2021

In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm ... more In this paper, we propose a predictor-corrector type Consensus Based Optimization(CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in a asset-bundle which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value.

Journal of Mathematical Analysis and Applications, Mar 1, 1999

The existence and the regularity of Young measure-valued solutions to non-Newtonian flows are con... more The existence and the regularity of Young measure-valued solutions to non-Newtonian flows are considered. Furthermore, the uniqueness of solutions and their asymptotic behavior are given.

Mathematical Methods in The Applied Sciences, Jul 15, 2019

In this paper, we study stochastic aggregation properties of the financial model for the N‐asset ... more In this paper, we study stochastic aggregation properties of the financial model for the N‐asset price process whose dynamics is modeled by the weakly geometric Brownian motions with stochastic drifts. For the temporal evolution of stochastic components of drift coefficients, we employ a stochastic first‐order Cucker‐Smale model with additive noises. The asset price processes are weakly interacting via the stochastic components of drift coefficients. For the aggregation estimates, we use the macro‐micro decomposition of the fluctuations around the average process and show that the fluctuations around the average value satisfies a practical aggregation estimate over a time‐independent symmetric network topology so that we can control the differences of drift coefficients by tuning the coupling strength. We provide numerical examples and compare them with our analytical results. We also discuss some financial implications of our proposed model.

Applied Mathematics and Computation, Mar 1, 1992

... We normalize the system by the transformation ak x 1 Cos B sin 0 2 rc k KV = 1 cyd sin 0 cos ... more ... We normalize the system by the transformation ak x 1 Cos B sin 0 2 rc k KV = 1 cyd sin 0 cos B 0 1 Se 1 a (3.8) c with K=c 4c(l+k)c2(1+k)2, 0=arctan[ K k+2)]+7r, and a general scale factor d = Vc I a Q(1 c) [(1 c) ]. Rescaling time to t = t 2 K , (2. 8) reduces to dt y PL Yj +[ x]' (3.9 ...

Annali Dell'universita' Di Ferrara, Sep 25, 2009

Networks and Heterogeneous Media, 2022

We propose a time-delayed Cucker-Smale type model(CS model), which can be applied to modeling (1)... more We propose a time-delayed Cucker-Smale type model(CS model), which can be applied to modeling (1) collective dynamics of self-propelling agents and (2) the dynamical system of stock return volatility in a financial market. For both models, we assume that it takes a certain amount of time to collect/process information about the current position/return configuration until velocity/volatility adjustment is made. We provide a sufficient condition under which flocking phenomena occur. We also identify the initial configuration for a two-agent case, in which collective behaviors are accelerated by changes in the delay parameter. Numerical illustrations and financial simulations are carried out to verify the validity of the model.

Social Science Research Network, 2020

Time delay in communication(information) flow is often found in many network systems. Inspired by... more Time delay in communication(information) flow is often found in many network systems. Inspired by volatility spillovers and clustering explained by “flocking” mechanism, we study the effect of the time delay in our model system of heterogeneous stock returns’ volatilities. Our model is a stochastic multi-volatility model in which a volatility’s dynamics is conditional on its value relative to others. Due to the finite speed of propagation, the dynamics is updated by volatilities’ one-to-one relationship with a short time delay. Our theoretical framework is sufficient to show the exponential convergence of volatilities toward the constant asymptotic value. When time delay is considered, convergence happens faster with lower variance than that in the model without time delay.

한국산업응용수학회 학술대회 논문집, May 1, 2012

A hybrid numerical method is studied for pricing options that linked to several equities. Instead... more A hybrid numerical method is studied for pricing options that linked to several equities. Instead of imposing artificial boundary condition for the multi-dimensional Black-Scholes equation, we calculate certain low-dimensional model equation at each time-step using pre-simulated Monte-Carlo(MC) time series. With standard finite difference method using nine point stencil, our method reduce the computational domain of the governing equation (the two dimensional Black-Scholes equation) exceedingly.As benchmark tests,we consider the call on themaximum option which has an analytic solution, and a complicated structured note from the derivative market.

Houston Journal of Mathematics, 2000

ABSTRACT

Quarterly of Applied Mathematics, Jun 1, 2000

The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonia... more The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonian flows are considered. Galerkin approximation and an L2 compactness theorem are main ingredients for the proof of the existence of Young measurevalued solutions. Under a certain convexity condition for the energy, we prove that Young measure-valued solutions are weak solutions. Also, for the limited cases, we prove a regularity theorem.

Journal of Statistical Physics, Aug 29, 2019

In this paper, we study the herding phenomena in financial markets arising from the combined effe... more In this paper, we study the herding phenomena in financial markets arising from the combined effect of (1) non-coordinated collective interactions between the market players and (2) concurrent reactions of market players to dynamic market signals. By interpreting the expected rate of return of an asset and the favorability on that asset as position and velocity in phase space, we construct an agent-based particle model for herding behavior in finance. We then define two types of herding functionals using this model, and show that they satisfy a Gronwall type estimate and a LaSalle type invariance property respectively, leading to the herding behavior of the market players. Various numerical tests are presented to numerically verify these results.

Journal of Statistical Physics, May 6, 2019

As a continuation of the study of the herding model proposed in [2], we consider in this paper th... more As a continuation of the study of the herding model proposed in [2], we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the meanfield limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat's lemma. We, however, don't get any herding rate in this case. On the other hand, we also establish a Grönwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.

Mathematical Methods in The Applied Sciences, Sep 4, 2020

We study the stochastic aggregation of linearly coupled Cucker-Smale (CS) particles on several as... more We study the stochastic aggregation of linearly coupled Cucker-Smale (CS) particles on several asymmetric networks. Our proposed first-order stochastic CS model was motivated as a stochastic dynamics modeling on the rates of multiasset return. In this study, we consider three asymmetric networks and study sufficient conditions toward stochastic aggregation for each proposed network. We also provide several numerical and empirical examples and compare them with theoretical results. In financial applications, we regard particles or agents as analysts and study their herding behavior based on our proposed model.

Physica D: Nonlinear Phenomena, Feb 1, 2022

Discrete and Continuous Dynamical Systems-series B, 2008

Page 1. DISCRETE AND CONTINUOUS Website: http://aimSciences.org DYNAMICAL SYSTEMS SERIES B Volume... more Page 1. DISCRETE AND CONTINUOUS Website: http://aimSciences.org DYNAMICAL SYSTEMS SERIES B Volume 10, Number 1, July 2008 pp. 1–18 ESTIMATES OF THE WAKE FOR THE 3D OSEEN EQUATIONS Hyeong ...

Journal of Mathematical Analysis and Applications, May 1, 2002

We first show the analyticity of Stokes operator in a weighted space L p γ (R 3 +). We also show ... more We first show the analyticity of Stokes operator in a weighted space L p γ (R 3 +). We also show that the Hodge decomposition holds on L p γ (R 3 +). Then, we estimate the asymptotic behavior of the Stokes solutions in space and time directions. For 1 < r q < ∞, if t is large enough, then R 3 + |u(x, t)| q ω(x) γ q dx

Mathematical Models and Methods in Applied Sciences, May 13, 2013

In this study, we present a new stochastic volatility model incorporating a flocking mechanism be... more In this study, we present a new stochastic volatility model incorporating a flocking mechanism between individual volatilities of assets. Collective phenomena of asset pricing and volatilities in financial markets are often observed; these phenomena are more apparent when the market is in critical situations (market crashes). In the classical Heston model, the constant theoretical mean of the square of the volatility was employed, which can be assumed a priori. Our proposed model does not assume this mean value a priori, we instead use the flocking effect to continuously update the theoretical mean value using the local weighted average of individual volatility values. To perform this function, we use the Cucker–Smale flocking mechanism to calculate the local mean. For some classes of interaction weights such as all-to-all and symmetric coupling with a positive lower bound, we show that the fluctuations of the square process of volatility are uniformly bounded, such that the overall dynamics are mainly dictated by the averaged process. We also provide several numerical examples showing the dynamics of volatility.

Nonlinear Analysis-theory Methods & Applications, Jul 1, 2023

한국산업응용수학회 학술대회 논문집, May 1, 2006

Here, Ω is the exterior domain in R identified with the region filled by a viscous incompressible... more Here, Ω is the exterior domain in R identified with the region filled by a viscous incompressible fluid; ∂Ω denotes the boundary of Ω which is assumed to be a C∞ and compact hypersurface. The unknown variables u = (u1, u2, u3) and p denote the unknown velocity vector and pressure, a = (a1, a2, a3) denotes a given initial velocity. We consider the case lim|x|→∞ u(t, x) = 0 only. The case lim|x|→∞ u(t, x) = u∞ 6= 0 was studied by Kobayashi and Shibata [23] and Shibata [30] in the same spirit. We also consider the Stokes approximation :