Constrained Quadratic Risk Minimization via Forward and Backward Stochastic Differential Equations

In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of FBSDEs together with other conditions. We characterise explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion and vice versa. We apply the results to solve quadratic risk minimization problems with cone-constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems.Comment: 22 page

Forward Performance Measurement with Applications in Indifference Valuation

In this thesis, we present basic ideas and key results for forward performance measurement. Besides, we provide an explicit construction of the optimal processes of a class of time-monotone forward performance processes. Moreover, starting with a two parameter family risk tolerance function, we construct a class of forward performance processes. By letting the parameter go to zero, we obtain the forward exponential utility. Finally, using the forward exponential utility, we solve the integrated portfolio management problem by the so-called utility-based approach and compare it with its classical backward indifference counterpart

Stochastic maximum principle and dynamic convex duality in continuous-time constrained portfolio optimization

This thesis seeks to gain further insight into the connection between stochastic optimal control and forward and backward stochastic differential equations and its applications in solving continuous-time constrained portfolio optimization problems. Three topics are studied in this thesis. In the first part of the thesis, we focus on stochastic maximum principle, which seeks to establish the connection between stochastic optimal control and backward stochastic differential differential equations coupled with static optimality condition on the Hamiltonian. We prove a weak neccessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maxi- mum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarkes generalized gradient of the Hamiltonian and Clarkes normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle. In the second part of the thesis, we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach,we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of FBSDEs together with other conditions. We characterise explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion and vice versa. We apply the results to solve quadratic risk minimization problems with cone-constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems. In the final section of the thesis, we extend the previous result to utility maximization problems. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint processes coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also find that the optimal primal wealth process coincides with the optimal adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems and contrasts the simplicity of the duality approach we propose with the technical complexity in solving the primal problem directly.Open Acces

Least-squares finite-element lattice Boltzmann method

A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method’s geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow

Characterization of Bubble Transport in Porous Media Using a Microfluidic Channel

This study investigates the effect on varying flow rates and bubble sizes on gas–liquid flow through porous media in a horizontal microchannel. A simple bubble generation system was set up to generate bubbles with controllable sizes and frequencies, which directly flowed into microfluidic channels packed with different sizes of glass beads. Bubble flow was visualized using a high-speed camera and analyzed to obtain the change in liquid holdup. Pressure data were measured for estimation of hydraulic conductivity. The bubble displacement pattern in the porous media was viscous fingering based on capillary numbers and visual observation. Larger bubbles resulted in lower normalized frequency of the bubble breakthrough by 20 to 60 percent. Increasing the flow rate increased the change in apparent liquid holdup during bubble breakthrough. Larger bubbles and lower flow rate reduced the relative permeability of each channel by 50 to 57 percent and 30 to 64 percent, respectively

An Ensemble Multilabel Classification for Disease Risk Prediction

It is important to identify and prevent disease risk as early as possible through regular physical examinations. We formulate the disease risk prediction into a multilabel classification problem. A novel Ensemble Label Power-set Pruned datasets Joint Decomposition (ELPPJD) method is proposed in this work. First, we transform the multilabel classification into a multiclass classification. Then, we propose the pruned datasets and joint decomposition methods to deal with the imbalance learning problem. Two strategies size balanced (SB) and label similarity (LS) are designed to decompose the training dataset. In the experiments, the dataset is from the real physical examination records. We contrast the performance of the ELPPJD method with two different decomposition strategies. Moreover, the comparison between ELPPJD and the classic multilabel classification methods RAkEL and HOMER is carried out. The experimental results show that the ELPPJD method with label similarity strategy has outstanding performance

Intermittent Antibiotic Treatment Accelerated the Development of Colitis in IL-10 Knockout Mice

Many epidemiological studies suggest an association between antibiotic exposure and the development of inflammatory bowel disease [IBD]. However, the majority of these studies are observational and still the question remains, “Does the specific antibiotic administration regimen play a role in the development of colitis?” This study aimed to compare the possible effects of continuous and intermittent antibiotic exposure on the development of colitis using a colitis-susceptible IL-10 knockout [IL-10–/–] mouse model