Time management in a Poisson fishing model
Anna Karpowicz, Krzysztof Szajowski

TL;DR
This paper extends a fishing model to include two fishing spots with different fish catch processes, aiming to find optimal stopping times to maximize satisfaction within a fixed fishing period.
Contribution
It introduces a dual stopping time framework for a two-location fishing problem with different renewal processes and utility-cost considerations.
Findings
Derived the value function for the optimal stopping problem.
Established the optimal switching and stopping times.
Provided explicit solutions for the extended model.
Abstract
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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsProbability and Risk Models · Stochastic processes and statistical mechanics · Advanced Queuing Theory Analysis
