Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.Comment: 29 page

Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.Comment: 18 page

Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions

Abstract In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions

Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact

Abstract. In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime switching framework. The problem can be solved with the dynamic programming principle. The optimal value function is the unique continuous viscosity solution to the HJB equation and can be computed with the finite difference method

On-chip ultrasensitive and rapid hydrogen sensing based on plasmon-induced hot electron–molecule interaction

Hydrogen energy is a zero-carbon replacement for fossil fuels. However, hydrogen is highly flammable and explosive hence timely sensitive leak detection is crucial. Existing optical sensing techniques rely on complex instruments, while electrical sensing techniques usually operate at high temperatures and biasing condition. In this paper an on-chip plasmonic–catalytic hydrogen sensing concept with a concentration detection limit down to 1 ppm is presented that is based on a metal–insulator–semiconductor (MIS) nanojunction operating at room temperature and zero bias. The sensing signal of the device was enhanced by three orders of magnitude at a one-order of magnitude higher response speed compared to alternative non-plasmonic devices. The excellent performance is attributed to the hydrogen induced interfacial dipole charge layer and the associated plasmonic hot electron modulated photoelectric response. Excellent agreements were achieved between experiment and theoretical calculations based on a quantum tunneling model. Such an on-chip combination of plasmonic optics, photoelectric detection and photocatalysis offers promising strategies for next-generation optical gas sensors that require high sensitivity, low time delay, low cost, high portability and flexibility

Amplifier limited information rates in high-speed optical fiber communication systems

Due to the high transmission capacity, optical fiber systems have been widely applied in the modern telecommunication infrastructure to meet the ever-increasing demand of data traffic. Optical amplifiers have been employed to amplify optical signals and to compensate for the transmission losses. They play a key role in relaying the signals in ultra-wideband optical fiber communication systems. However, the amplified spontaneous emission (ASE) noise will be introduced and will pose constraints on the transmission information rates. The mutual information (MI) and the generalized mutual information (GMI) have been applied to evaluate the information rates in communication systems. In this work, we have investigated the impact of ASE noise on the MI and the GMI, and developed corresponding analyses across different modulation formats. Our work aims to explore the limit and requirements on optical amplifiers in next-generation ultra-wideband optical fiber communication systems

Association of IL-1beta gene polymorphism with cachexia from locally advanced gastric cancer

BACKGROUND: IL-1beta has been implicated in inflammatory episode. In view of the inflammatory nature of cancer cachexia, we determined the predictive value of IL-1B-31 T/C, -511 C/T, +3954 C/T and IL-1RN VNTR gene polymorphisms on the occurrence of cachexia associated with locally advanced gastric cancer. METHODS: The study included 214 patients and 230 healthy volunteers. Genomic DNA was prepared from peripheral blood leukocytes. Genotypes and allele frequencies were determined in patients and healthy controls using restriction fragment length polymorphism analysis of polymerase chain reaction products. RESULTS: The overall frequencies of IL-1B-31 T, -511 T, +3954 T and IL-1RN VNTR alleles in patients with locally advanced gastric cancer were all comparable with those in controls. No significant differences were found in the distribution of IL-1B-31 T, -511 T and IL-1RN VNTR between patients with cachexia and without. Patients with cachexia showed a significantly higher prevalence of IL-1B+3954 T allele than those without (P = 0.018). In a logistic regression analysis adjusted for actual weight, carcinoma location and stage, the IL-1B+3954 CT genotype was associated with an odds ratio of 2.512 (95% CI, 1.180 – 5.347) for cachexia. CONCLUSION: The IL-1B+3954 T allele is a major risk for cachexia from locally gastric cancer. Genetic factors studied are not likely to play an important role in the determination of susceptibility to locally advanced gastric cancer