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 Title
 A PRICEVOLUME MODEL FOR A SINGLEPERIOD STOCK MARKET.
 Creator

ChenShue, Yun, Yong, Jiongmin, University of Central Florida
 Abstract / Description

The intention of this thesis is to provide a primitive mathematical model for a financial market in which tradings affect the asset prices. Currently, the idea of a pricevolume relationship is typically used in the form of empirical models for specific cases. Among the theoretical models that have been used in stock markets, few included the volume parameter. The thesis provides a general theoretical model with the volume parameter for the intention of a broader use. The core of the model is...
Show moreThe intention of this thesis is to provide a primitive mathematical model for a financial market in which tradings affect the asset prices. Currently, the idea of a pricevolume relationship is typically used in the form of empirical models for specific cases. Among the theoretical models that have been used in stock markets, few included the volume parameter. The thesis provides a general theoretical model with the volume parameter for the intention of a broader use. The core of the model is the correlation between trading volume and stock price, indicating that volume should be a function of the stock price and time. This function between price and time was made visible by the use of the trading volume process, also known as the Limit Order book. The development of this model may be of some use to investors, who could build their wealth process based on the dynamics of the process found through a Limit Order Book. This wealth process can help them build an optimal trading strategy design.
Show less  Date Issued
 2014
 Identifier
 CFH0004689, ucf:45245
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFH0004689
 Title
 PRICE DISCOVERY IN THE U.S. BOND MARKETS: TRADING STRATEGIES AND THE COST OF LIQUIDITY.
 Creator

Shao, Haimei, Yong, Jiongmin, University of Central Florida
 Abstract / Description

The world bond market is nearly twice as large as the equity market. The goal of this dissertation is to study the dynamics of bond price. Among the liquidity risk, interest rate risk and default risk, this dissertation will focus on the liquidity risk and trading strategy. Under the mathematical frame of stochastic control, we model price setting in U.S. bond markets where dealers have multiple instruments to smooth inventory imbalances. The difficulty in obtaining the optimal trading...
Show moreThe world bond market is nearly twice as large as the equity market. The goal of this dissertation is to study the dynamics of bond price. Among the liquidity risk, interest rate risk and default risk, this dissertation will focus on the liquidity risk and trading strategy. Under the mathematical frame of stochastic control, we model price setting in U.S. bond markets where dealers have multiple instruments to smooth inventory imbalances. The difficulty in obtaining the optimal trading strategy is that the optimal strategy and value function depend on each other, and the corresponding HJB equation is nonlinear. To solve this problem, we derived an approximate optimal explicit trading strategy. The result shows that this trading strategy is better than the benchmark central symmetric trading strategy.
Show less  Date Issued
 2011
 Identifier
 CFE0003633, ucf:48858
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003633
 Title
 Filtering Problems in Stochastic Tomography.
 Creator

Gomez, Tyler, Swanson, Jason, Yong, Jiongmin, Tamasan, Alexandru, Dogariu, Aristide, University of Central Florida
 Abstract / Description

Distinguishing signal from noise has always been a major goal in probabilistic analysis of data. Such is no less the case in the field of medical imaging, where both the processes of photon emission and their rate of absorption by the body behave as random variables. We explore methods by which to extricate solid conclusions from noisy data involving an Xray transform, long the mathematical mainstay of such tools as computed axial tomography (CAT scans). Working on the assumption of having...
Show moreDistinguishing signal from noise has always been a major goal in probabilistic analysis of data. Such is no less the case in the field of medical imaging, where both the processes of photon emission and their rate of absorption by the body behave as random variables. We explore methods by which to extricate solid conclusions from noisy data involving an Xray transform, long the mathematical mainstay of such tools as computed axial tomography (CAT scans). Working on the assumption of having some prior probabilities assigned to various states a body can be found in, we introduce and make rigorous an understanding of how to condition these into posterior probabilities by using the scan data.
Show less  Date Issued
 2017
 Identifier
 CFE0006740, ucf:51839
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006740
 Title
 Optimization problem in single period markets.
 Creator

Jiang, Tian, Yong, Jiongmin, Qi, Yuanwei, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

There had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal...
Show moreThere had been a number of researches that investigated on the security market without transactioncosts. The focus of this research is in the area that when the security market with transaction costsis fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal.The research approach adopted in this thesis includes linear algebra and elementary probability.The thesis provides evidence that we can maximize expected utility function to achieve our goal(maximize expected return under certain risk tolerance). The main conclusions drawn from thisstudy are under certain conditions the security market is arbitragefree, and we can always find anoptimal portfolio maximizing certain expected utility function.
Show less  Date Issued
 2013
 Identifier
 CFE0004696, ucf:49875
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004696
 Title
 Valuation of OverTheCounter (OTC) Derivatives with Collateralization.
 Creator

Guerrero, Leon, Yong, Jiongmin, Li, Xin, Brennan, Joseph, University of Central Florida
 Abstract / Description

Collateralization in overthecounter (OTC) derivatives markets has grown rapidly overthe past decade, and even faster in the past few years, due to the impact of the recentfinancial crisis and the particularly important attention to the counterparty credit risk in derivatives contracts. The addition of collateralization to such contracts significantly reduces the counterparty credit risk and allows to offset liabilities in case of default.We study the problem of valuation of OTC derivatives...
Show moreCollateralization in overthecounter (OTC) derivatives markets has grown rapidly overthe past decade, and even faster in the past few years, due to the impact of the recentfinancial crisis and the particularly important attention to the counterparty credit risk in derivatives contracts. The addition of collateralization to such contracts significantly reduces the counterparty credit risk and allows to offset liabilities in case of default.We study the problem of valuation of OTC derivatives with payoff in a single currencyand with single underlying asset for the cases of zero, partial, and perfect collateralization. We assume the derivative is traded between two defaultfree counterparties and analyze the impact of collateralization on the fair present value of the derivative. We establish a uniform generalized derivative pricing framework for the three cases of collateralization and show how different approaches to pricing turn out to be consistent. We then generalize the results to include multiasset and crosscurrency arguments, where the underlyingand the derivative are in some domestic currency, but the collateral is posted in a foreign currency. We show that the results for the single currency, multiasset case are consistent with those obtained for the single currency, single asset case.
Show less  Date Issued
 2013
 Identifier
 CFE0004855, ucf:49688
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004855
 Title
 Multilevel Optimization and Applications with NonTraditional Game Theory.
 Creator

Yun, Guanxiang, Zheng, Qipeng, Boginski, Vladimir, Karwowski, Waldemar, Yong, Jiongmin, University of Central Florida
 Abstract / Description

We study multilevel optimization problem on energy system, transportation system and information network. We use the concept of boundedly rational user equilibrium (BRUE) to predict the behaviour of users in systems. By using multilevel optimization method with BRUE, we can help to operate the system work in a more efficient way. Based on the introducing of model with BRUE constraints, it will lead to the uncertainty to the optimization model. We generate the robust optimization as the...
Show moreWe study multilevel optimization problem on energy system, transportation system and information network. We use the concept of boundedly rational user equilibrium (BRUE) to predict the behaviour of users in systems. By using multilevel optimization method with BRUE, we can help to operate the system work in a more efficient way. Based on the introducing of model with BRUE constraints, it will lead to the uncertainty to the optimization model. We generate the robust optimization as the multilevel optimization model to consider for the pessimistic condition with uncertainty. This dissertation mainly includes four projects. Three of them use the pricing strategy as the first level optimization decision variable. In general, our models' first level's decision variables are the measures that we can control, but the second level's decision variables are users behaviours that can only be restricted within BRUE with uncertainty.
Show less  Date Issued
 2019
 Identifier
 CFE0007881, ucf:52758
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007881
 Title
 Sampling and Reconstruction of Spatial Signals.
 Creator

Cheng, Cheng, Li, Xin, Sun, Qiyu, Yong, Jiongmin, Liu, Zhe, Xu, Mengyu, University of Central Florida
 Abstract / Description

Digital processing of signals f may start from sampling on a discrete set ?, f ?? f(?_n), ?_n ??.The sampling theory is one of the most basic and fascinating topics in applied mathematics and in engineering sciences. The most well known form is the uniform sampling theorem for bandlimited/wavelet signals, that gives a framework for converting analog signals into sequences of numbers. Over the past decade, the sampling theory has undergone a strong revival and the standard sampling paradigm...
Show moreDigital processing of signals f may start from sampling on a discrete set ?, f ?? f(?_n), ?_n ??.The sampling theory is one of the most basic and fascinating topics in applied mathematics and in engineering sciences. The most well known form is the uniform sampling theorem for bandlimited/wavelet signals, that gives a framework for converting analog signals into sequences of numbers. Over the past decade, the sampling theory has undergone a strong revival and the standard sampling paradigm is extended to nonbandlimited signals including signals in reproducing kernel spaces (RKSs), signals with finite rate of innovation (FRI) and sparse signals, and to nontraditional sampling methods, such as phaseless sampling.In this dissertation, we first consider the sampling and Galerkin reconstruction in a reproducing kernel space. The fidelity measure of perceptual signals, such as acoustic and visual signals, might not be well measured by least squares. In the first part of this dissertation, we introduce a fidelity measure depending on a given sampling scheme and propose a Galerkin method in Banach space setting for signal reconstruction. We show that the proposed Galerkin method provides a quasioptimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximationprojection algorithm in a reproducing kernel subspace of Lp.A spatially distributed network contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed networks for signal sampling and reconstruction. We introduce a graph structure for a distributed sampling and reconstruction system by coupling agents in a spatially distributed network with innovative positions of signals. We split a distributed sampling and reconstruction system into a family of overlapping smaller subsystems, and we show that the stability of the sensing matrix holds if and only if its quasirestrictions to those subsystems have l_2 uniform stability. This new stability criterion could be pivotal for the design of a robust distributed sampling and reconstruction system against supplement, replacement and impairment of agents, as we only need to check the uniform stability of affected subsystems. We also propose an exponentially convergent distributed algorithm for signal reconstruction, that provides a suboptimal approximation to the original signal in the presence of bounded sampling noises.Phase retrieval (Phaseless Sampling and Reconstruction) arises in various fields of science and engineering. It consists of reconstructing a signal of interest from its magnitude measurements. Sampling in shiftinvariant spaces is a realistic model for signals with smooth spectrum. We consider phaseless sampling and reconstruction of realvalued signals in a shiftinvariant space from their magnitude measurements on the whole Euclidean space and from their phaseless samples taken on a discrete set with finite sampling density. We find an equivalence between nonseparability of signals in a shiftinvariant space and their phase retrievability with phaseless samples taken on the whole Euclidean space. We also introduce an undirected graph to a signal and use connectivity of the graph to characterize the nonseparability of highdimensional signals. Under the local complement property assumption on a shiftinvariant space, we find a discrete set with finite sampling density such that signals in shiftinvariant spaces, that are determined by their magnitude measurements on the whole Euclidean space, can be reconstructed in a stable way from their phaseless samples taken on that discrete set. We also propose a reconstruction algorithm which provides a suboptimal approximation to the original signal when its noisy phaseless samples are available only.
Show less  Date Issued
 2017
 Identifier
 CFE0006726, ucf:51889
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006726
 Title
 HJB Equation and Statistical Arbitrage applied to High Frequency Trading.
 Creator

Park, Yonggi, Yong, Jiongmin, Swanson, Jason, Richardson, Gary, Shuai, Zhisheng, University of Central Florida
 Abstract / Description

In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the HamiltonJacobiBellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.
 Date Issued
 2013
 Identifier
 CFE0004907, ucf:49628
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004907
 Title
 Calibration of Option Pricing in Reproducing Kernel Hilbert Space.
 Creator

Ge, Lei, Nashed, M, Yong, Jiongmin, Qi, Yuanwei, Sun, Qiyu, Caputo, Michael, University of Central Florida
 Abstract / Description

A parameter used in the BlackScholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be illposed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing...
Show moreA parameter used in the BlackScholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be illposed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. We discuss the existence of the minimizer by using regu larized reproducing kernel method and show that the regularizer resolves the numerical instability of the calibration problem. Finally, we apply our studied method to data sets of index options by simulation tests and discuss the empirical results obtained.
Show less  Date Issued
 2015
 Identifier
 CFE0005617, ucf:50211
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005617
 Title
 Differential Games for MultiAgent Systems under Distributed Information.
 Creator

Lin, Wei, Qu, Zhihua, Simaan, Marwan, Haralambous, Michael, Das, Tuhin, Yong, Jiongmin, University of Central Florida
 Abstract / Description

In this dissertation, we consider differential games for multiagent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multiplayer pursuitevasion games, etc. Since the admissible strategy of each agent has to conform to the information...
Show moreIn this dissertation, we consider differential games for multiagent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multiplayer pursuitevasion games, etc. Since the admissible strategy of each agent has to conform to the information graph constraint, the conventional game strategy design approaches based upon Riccati equation(s) are not applicable because all the agents are required to have the information of the entire system. Accordingly, the game strategy design under distributed information is commonly known to be challenging. Toward this end, we propose novel openloop and feedback game strategy design approaches for Nash equilibrium and noninferior solutions with a focus on linear quadratic differential games. For the openloop design, approximate Nash/noninferior game strategies are proposed by integrating distributed state estimation into the openloop globalinformation Nash/noninferior strategies such that, without global information, the distributed game strategies can be made arbitrarily close to and asymptotically converge over time to the globalinformation strategies. For the feedback design, we propose the best achievable performance indices based approach under which the distributed strategies form a Nash equilibrium or noninferior solution with respect to a set of performance indices that are the closest to the original indices. This approach overcomes two issues in the classical optimal output feedback approach: the simultaneous optimization and initial state dependence. The proposed openloop and feedback design approaches are applied to an unmanned aerial vehicle formation control problem and a multipursuer singleevader differential game problem, respectively. Simulation results of several scenarios are presented for illustration.
Show less  Date Issued
 2013
 Identifier
 CFE0005025, ucf:49991
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005025