Search

This paper studies an optimal consumption-investment problem for an investor whose instantaneous utility depends on both consumption and wealth, and the investor faces a general borrowing constraint that the investment amount in the risky asset does not exceed an exogenous function of the wealth. We show that the value function is second-order smooth and present the optimal consumption-investment policy in a feedback form. Moreover, when the risky investment amount is bounded above by a fixed constant, we show that under certain conditions, the constraint is binding if and only if an endogenous threshold bounds the portfolio wealth, and we determine the endogenous wealth threshold with the smooth fit condition. Our results encompass several well-developed portfolio choice models and imply new applications., Comment: 35 pages

This paper demonstrates the additive and multiplicative version of a long-run law of unexpected shocks for any economic variable. We derive these long-run laws by the martingale theory without relying on the stationary and ergodic conditions. We apply these long-run laws to asset return, risk-adjusted asset return, and the pricing kernel process and derive new asset pricing implications. Moreover, we introduce several dynamic long-term measures on the pricing kernel process, which relies on the sample data of asset return. Finally, we use these long-term measures to diagnose leading asset pricing models., Comment: 42 pages

Although deep convolution neural networks (DCNN) have achieved excellent performance in human pose estimation, these networks often have a large number of parameters and computations, leading to the slow inference speed. For this issue, an effective solution is knowledge distillation, which transfers knowledge from a large pre-trained network (teacher) to a small network (student). However, there are some defects in the existing approaches: (I) Only a single teacher is adopted, neglecting the potential that a student can learn from multiple teachers. (II) The human segmentation mask can be regarded as additional prior information to restrict the location of keypoints, which is never utilized. (III) A student with a small number of parameters cannot fully imitate heatmaps provided by datasets and teachers. (IV) There exists noise in heatmaps generated by teachers, which causes model degradation. To overcome these defects, we propose an orderly dual-teacher knowledge distillation (ODKD) framework, which consists of two teachers with different capabilities. Specifically, the weaker one (primary teacher, PT) is used to teach keypoints information, the stronger one (senior teacher, ST) is utilized to transfer segmentation and keypoints information by adding the human segmentation mask. Taking dual-teacher together, an orderly learning strategy is proposed to promote knowledge absorbability. Moreover, we employ a binarization operation which further improves the learning ability of the student and reduces noise in heatmaps. Experimental results on COCO and OCHuman keypoints datasets show that our proposed ODKD can improve the performance of different lightweight models by a large margin, and HRNet-W16 equipped with ODKD achieves state-of-the-art performance for lightweight human pose estimation.

This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the optimal investment strategy under the specific condition on model parameters in terms of second-order ordinary differential equations. We demonstrate an endogenous number that measures the expected value to sustain the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio's value is higher than this number; but, if the portfolio is not worth enough to sustain the retirement spending, the retiree actively invests in the stock market for the higher expected return. Besides, we solve an optimal portfolio choice problem under a leverage constraint and show that the optimal portfolio would lose significantly in stressed markets. This paper shows that the time-varying risk capacity constraint has important implications for asset allocation in retirement.