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

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

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

Tunable hysteresis effect for perovskite solar cells

Perovskite solar cells (PSCs) usually suffer from a hysteresis effect in current–voltage measurements, which leads to an inaccurate estimation of the device e fficiency. Although ion migration, charge trapping/ detrapping, and accumulation have been proposed as a b asis for the hysteresis, the origin of the hysteresis has not been apparently unraveled. Herein we reporte d a tunable hysteresis effect based uniquely on open- circuit voltage variations in printable mesos copic PSCs with a simplified triple-layer TiO 2 /ZrO 2 /carbon architecture. The electrons are collected by the compact TiO 2 /mesoporous TiO 2 (c-TiO 2 /mp-TiO 2 )bilayer, and the holes are collected by the carbon layer. By adj usting the spray deposition cycles for the c-TiO 2 layer andUV-ozonetreatment,weachievedhysteresis-norm al, hysteresis-free, and hysteresis-inverted PSCs. Such unique trends of tunable hysteresis are anal yzed by considering the polarization of the TiO 2 /perovskite interface, which can accumulate positive charges reversibly. Successfully tuning of the hysteresis effect clarifies the critical importance of the c-TiO 2 /perovskite interface in controlling the hysteretic trends observed, providing important insights towards the understanding of this rapidly developing photovoltaic technology

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

Joyful: Joint Modality Fusion and Graph Contrastive Learning for Multimodal Emotion Recognition

Multimodal emotion recognition aims to recognize emotions for each utterance of multiple modalities, which has received increasing attention for its application in human-machine interaction. Current graph-based methods fail to simultaneously depict global contextual features and local diverse uni-modal features in a dialogue. Furthermore, with the number of graph layers increasing, they easily fall into over-smoothing. In this paper, we propose a method for joint modality fusion and graph contrastive learning for multimodal emotion recognition (Joyful), where multimodality fusion, contrastive learning, and emotion recognition are jointly optimized. Specifically, we first design a new multimodal fusion mechanism that can provide deep interaction and fusion between the global contextual and uni-modal specific features. Then, we introduce a graph contrastive learning framework with inter-view and intra-view contrastive losses to learn more distinguishable representations for samples with different sentiments. Extensive experiments on three benchmark datasets indicate that Joyful achieved state-of-the-art (SOTA) performance compared to all baselines