Optimal Control

Consider a fishing optimal control problem which is defined by Pt = a + bpt − xt… [Full question continued]

Introduction This question involves an optimal control problem in the context of renewable resource management—specifically, the fishing industry. The goal is to determine the optimal harvesting strategy (xt) that maximizes utility over time while accounting for population dynamics of the fish stock. We are also asked to derive the transversality condition and solve for the […]

Consider a fishing optimal control problem which is defined by Pt = a + bpt − xt… [Full question continued] Read More »

Consider an investor who at time t = 0 is endowed with initial capital of x(0)=x0 > 0… [Full question continued]

Introduction This problem describes an optimal control problem in economics, specifically dealing with intertemporal consumption decisions made by an investor. The goal is to choose a consumption function c(t) over time interval [0, T] that maximizes utility from consumption while ensuring the investor remains solvent over time, meaning that capital remains positive. Let’s break it

Consider an investor who at time t = 0 is endowed with initial capital of x(0)=x0 > 0… [Full question continued] Read More »

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