Maximization of Wealth in a Jump-Diffusion Model

This paper study the problem of  wealth optimization when jump-diffusion asset price model being driven by a count process that more general than Poisson process. It is found unique equivalent martingale measure, we employ the conventional stochastic analysis methods. It is proved that the existence of an optimal portfolio and consumption process. The optimal wealth process, the value function, the optimal portfolio and consumption process are given

Modeling the Schedules Designed Interactions the Big River Trip Simulation

In this paper, we propose the schedules designed for different tour trips along the Big Long River. We build three models on the basis of the characteristics of drifts, that is: the model based on maximum effective coefficient, the model based on optimization the utilization of the camping sites, the model based on the distribution of camping sites for motorizes boats. According to our analysis, there are certain relationships with the number of tourists on the river at present, the number of newly-launching tourists, the number of tourists finishing their journey and the number of previous tourists on the river. Making use of the method of iteration, we construct the model based on maximum effective coefficient to maximum the effective coefficient and to reach the minimum contact. Introducing 0-1 variables ant colony algorithm, total launching tours every day, the transport choice and each tour group sailing days are available

An exact solution of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits

An exact solution of nuclear spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits is presented. The extended one-variable Heine-Stieltjes polynomials associated to the Bethe ansatz equations of the solution are determined, of which the sets of the zeros give the solution of the model, and can be determined relatively easily. A comparison of the solution to that of the standard pairing interaction with constant interaction strength among pairs in any orbit is made. It is shown that the overlaps of eigenstates of the model with those of the standard pairing model are always large, especially for the ground and the first excited state. However, the quantum phase crossover in the non-separable pairing model cannot be accounted for by the standard pairing interaction.Comment: 5 pages, 1 figure, LaTe

Water Cycle Process Research: Experiments and Observations

The evaluation of methods and instrumentation for measuring water cycle parameters and for monitoring the status of hydrological process will assist governmental personnel, researchers, and water resources practitioners in determining strategies for field and laboratory measurements. This chapter aims to specify the instruments and techniques developed during the long-term monitoring phase of field experimental stations and the establishment phase of indoor experimental laboratory in the Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences. The two field experimental stations, Dongtaigou and Chongling, have been initiated to observe and quantify the water cycle process for more than 10 years, which has formed a complete set of observing and experimental methods in watershed. The experimental laboratory is a new integrated water cycle experiment platform, based on the new technology integrated control, measurement, sensors, and information processing. It includes artificial rainfall system, experimental sink of runoff and erosion, river simulation system, and transformation dynamical processes experimental device among precipitation, vegetation water, surface water, soil water, and groundwater. The continued instrumentation development and advanced experimental strategies will serve as a first port of call for professionals studying the behavior of water footprint

Option Pricing Model With Continuous Dividends

This paper discusses the problem of pricing on European options in jump-diffusion model by martingale method. We assuming jump process are more commen then Possion process a kind of nonexplosive counting process. Supposing that the dividend for each share of the security is paid continuously in time at a rate equal to a fixed fraction of the price of the security. By changing the basic assumption of R.C.Merton option pricing model to the assumption. It is established that the behavior model of the stock pricing process is jump-diffusion process. With risk-neutral martingale measure, pricing formula and put-call parity for European options with continuous dividends are obtained by stochastic analysis method. The results of Margrabe are generalized

Wilson-loop One-point Functions in ABJM Theory

In this paper we initiate the study of correlation functions of a single trace operator and a circular supersymmetric Wilson loop in ABJM theory. The single trace operator is in the scalar sector and is an eigenstate of the planar two-loop dilatation operator. The Wilson loop is in the fundamental representation of the gauge group or a suitable (super-)group. Such correlation functions at tree level can be written as an overlap of the Bethe state corresponding to the single trace operator and a boundary state which corresponds to the Wilson loop. There are various type of supersymmetric Wilson loops in ABJM theory. We show that some of them correspond to integrable boundary states while some are not. For the integrable ones, we prove their integrability and obtain analytic formula for the overlaps. For the non-integrable ones, we give examples of non-vanishing overlaps for Bethe states which violate selection rules.Comment: 32 pages, 3 figure

Image Quality Is Not All You Want: Task-Driven Lens Design for Image Classification

In computer vision, it has long been taken for granted that high-quality images obtained through well-designed camera lenses would lead to superior results. However, we find that this common perception is not a "one-size-fits-all" solution for diverse computer vision tasks. We demonstrate that task-driven and deep-learned simple optics can actually deliver better visual task performance. The Task-Driven lens design approach, which relies solely on a well-trained network model for supervision, is proven to be capable of designing lenses from scratch. Experimental results demonstrate the designed image classification lens (``TaskLens'') exhibits higher accuracy compared to conventional imaging-driven lenses, even with fewer lens elements. Furthermore, we show that our TaskLens is compatible with various network models while maintaining enhanced classification accuracy. We propose that TaskLens holds significant potential, particularly when physical dimensions and cost are severely constrained.Comment: Use an image classification network to supervise the lens design from scratch. The final designs can achieve higher accuracy with fewer optical element