Stochastic optimization model of aquacultured fish for sale and ecological education

Abstract

A stochastic optimization model for management of aquacultured fish for sale and ecological education is established. Population dynamics of the fish is described with a system of stochastic differential equations assuming that they are stochastically harvested after an opening time: the variable to be optimized. A remarkable difference between the present and conventional models for the aquaculture is that the former considers the harvesting for ecological education, which is a key for current inland fishery especially in Japan. Finding the cost-effective optimal opening time effectively reduces to solving an algebraic equation. Mathematical analysis on the optimal opening time clearly reveals its unique existence and qualitative behavior, such as its dependence on the model parameters, which have practical implications. A demonstrative application example of the model is also presented focusing on an aquaculture of Plecoglossus altivelis in Japan.

Stochastic differential game for management of non-renewable fishery resource under model ambiguity

“…The first term represents the utility by harvesting the fish, which is assumed to be concave and increasing with respect to the biomass N s X s , having the form of the conventional Constant Relative Risk Aversion (CRRA) utility function widely-used in financial problems [5,38,55]. As in the case of P. altivelis in Japan, the harvested fish would be eaten by anglers, sold in market, or used for ecological education to the residents in some cases [74]. This term therefore evaluates economic, ecological, and social utilities of the harvesting in a lumped manner.…”

Existence and uniqueness of solutions for stochastic urban-population growth model

“…Researchers have become interested in stochastic differential equations for modeling population dynamics because these equations have proved to be useful in a variety of applications, such as in epidemics [5][6][7], fish population [8], phytoplankton concentration [9], HIV (virus) dynamics [10,11], dengue [12], and tumor cell growth [13]. Researchers have even considered the stochastic version of the deterministic tworegion population dynamics shown in (1) [e.g., [14][15][16]].…”

Mathematical and Computational Approaches for Stochastic Control of River Environment and Ecology: From Fisheries Viewpoint

“…Notice that fishery resources management problems in seas have conventionally been studied as both stochastic and deterministic optimal control problems (Reed 1988; do Val et al 2019; Kvamsdal et al 2016; Kvamsdal et al 2020), possibly because of their huge impacts on food and economy worldwide. On the other hand, the problems in inland waters usually have smaller impacts; nevertheless, they have been serving as unique elements to sustain local ecosystems, societies, and sometimes ecological education (Yoshioka and Yaegashi 2017). In addition, as we will demonstrate in this chapter, there exist many interesting associated management problems specific to inland fishery resources management.…”