Poisson捕鱼模型中的时间管理
Time management in a Poisson fishing model
摘要：
本文的目的是推广“钓鱼问题”的模型。简单的公式如下。钓鱼者去钓鱼。他买了一张固定时间的钓鱼票。湖边有两个钓鱼的地方。鱼类是根据两地不同的更新过程捕获的。鱼的重量和到达间隔时间由i.i.d.已知分布函数的随机变量。这些分布对于第一和第二捕鱼地点是不同的。垂钓者的满意度是由依赖于捕获鱼的大小的效用函数和与时间有关的费用函数之间的差给出的。在每一个地方，钓鱼者都有另一个效用函数和另一个费用函数。通过这种方式，钓鱼者对这两个地方的相对意见被建模。例如，在一个地方，可以以更大的概率捕获更好的鱼，或者其中一个地方更舒适。显然，我们的垂钓者希望有尽可能多的满意度，此外，他必须离开湖前固定的时刻。因此，他的目标是找到两个最佳的停时，以最大限度地提高他的满意度。第一次对应的时刻，当他最终应该改变的地方，第二次，当他应该停止捕鱼。这些停时必须小于固定的捕鱼时间。导出了问题的值和最优停时。
英文摘要：
The aim of the paper is to extend the model of "fishing problem". The simple formulation is following. The angler goes to fishing. He buys fishing ticket for a fixed time. There are two places for fishing at the lake. The fishes are caught according to renewal processes which are different at both places. The fishes' weights and the inter-arrival times are given by the sequences of i.i.d. random variables with known distribution functions. These distributions are different for the first and second fishing place. The angler's satisfaction measure is given by difference between the utility function dependent on size of the caught fishes and the cost function connected with time. On each place the angler has another utility functions and another cost functions. In this way, the angler's relative opinion about these two places is modeled. For example, on the one place better sort of fish can be caught with bigger probability or one of the places is more comfortable. Obviously our angler wants to have as much satisfaction as possible and additionally he have to leave the lake before the fixed moment. Therefore his goal is to find two optimal stopping times in order to maximize his satisfaction. The first time corresponds to the moment, when he eventually should change the place and the second time, when he should stop fishing. These stopping times have to be less than the fixed time of fishing. The value of the problem and the optimal stopping times are derived.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
