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In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications. Continuous-time models provide a powerful and elegant framework for solving stochastic optimization problems of finding the optimal contracts between two parties, under various assumptions on the information they have access to, and the effect they have on the underlying 'profit/loss' values. This monograph surveys recent results of the theory in a systematic way, using the approach of the so-called Stochastic Maximum Principle, in models driven by Brownian Motion. Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions.

We consider the problem of when to deliver the contract payoff, in a continuous-time principal-agent setting, in which the agent's effort is unobservable. The principal can design contracts of a simple form that induce the agent to ask for the payoff at the time of the principal's choosing. The optimal time of payment depends on the agent's and the principal's outside options. We develop a theory for general utility functions, while with CARA utilities we are able to specify conditions under which the optimal payment time is not random. However, in general, the optimal payment time is typically random. One illustrative application is the case when the agent can be fired, after having been paid a severance payment, and then replaced by another agent. The methodology we use is the stochastic maximum principle and its link to Forward-Backward Stochastic Differential Equations.

Object tracking is a crucial research subfield in computer vision and it has wide applications in navigation, robotics and military applications and so on. In this paper, the real-time visualization of 3D point clouds data based on the VLP-16 3D Light Detection and Ranging (LiDAR) sensor is achieved, and on the basis of preprocessing, fast ground segmentation, Euclidean clustering segmentation for outliers, View Feature Histogram (VFH) feature extraction, establishing object models and searching matching a moving spherical target, the Kalman filter and adaptive particle filter are used to estimate in real-time the position of a moving spherical target. The experimental results show that the Kalman filter has the advantages of high efficiency while adaptive particle filter has the advantages of high robustness and high precision when tested and validated on three kinds of scenes under the condition of target partial occlusion and interference, different moving speed and different trajectories. The research can be applied in the natural environment of fruit identification and tracking, robot navigation and control and other fields.