Stochastic Bioeconomics: A Review of Basic Methods and Results

Basic bioeconomic models which incorporate uncertainty are reviewed to show and compare the principal methods used and results reported in the literature. Beginning with a simple linear control model of stock uncertainty, we proceed to discuss more complex models which explicitly recognize risk preferences, firm and industry behavior, and market price effects. The effects of uncertainty on the results of bioeconomic analysis are rarely unambiguous, and in some instances differ little from corresponding deterministic results. This review is presented to enhance readers' appreciation of the papers to follow in this and the next issue of the journal.Environmental Economics and Policy, International Development, Resource /Energy Economics and Policy, Risk and Uncertainty,

On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model

This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.Comment: Key Words: Singular stochastic control, linear programming, relaxed contro

A General Approach to the Stochastic Rotation Problem with Amenity Valuation

This paper presents a new approach to study the optimal rotation policy with amenity valuation under uncertainty. We first postulate the stochastic forest value and assume plausibly that monetary value of amenities is a continuous and non-negative function of forest value thus presenting the trade-off between timber revenues and amenity values. Second, instead of using a dynamic programming approach, we derive a recursive representation of the total forest value and solve the optimal rotation threshold by applying ordinary non-linear programming techniques. Third, we characterize under certain set of conditions how the properties of both the expected cumulative value and the expected marginal cumulative value, accrued from amenity services, depend on the precise nature of the monetary valuation of amenities and what is the impact of volatility on these concepts. Finally, we illustrate our results explicitly in models based on logistic growth by focusing on the role of amenity valuation and volatility of forest value in the determination of Wicksellian and Faustmannian thresholds. Our theoretical and numerical findings emphasize the crucial importance of the nature of amenity valuation for the impact of higher volatility of forest value on the rotation thresholds.amenity valuation, optimal Faustmannian and Wicksellian rotation policy, stochatic impulse control

A Stochastic Bioeconomic Model with Research

This paper provides an incremental extension of a stochastic renewable resource model (Pindyck 1984) to include population dynamics research; i.e., the rate of accrual of information regarding the stochastic evolution of the stock, as a dynamic choice variable. While Pindyck models variance in stock growth as an exogenous parameter, our formulation endogenizes this variance and characterizes the impact of scientific information accrual on both the harvest decision and the present value of rents resulting from harvest activity. We illustrate the theoretical existence of an internal optimum in research effort using a numerical example.stochastic bioeconomic model, stochastic control, fisheries management, population dynamics research, renewable resource, uncertainty, Resource /Energy Economics and Policy, Q2, Q22, C61,

Population dynamical behavior of Lotka-Volterra system under regime switching

In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t); : : : ; xn(t))[(b(r(t)) + A(r(t))x(t))dt + (r(t))dB(t)]; where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction. We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain. The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients. Finally, the main results are illustrated by several examples

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Stochastic differential equation harvesting models: sustainable policies and profit optimization

We describe the growth dynamics of a fish or some other harvested population in a random environment using a stochastic differential equation ; general model, where the harvest term depends on a constant or on a variable fishing effort. We compare the profit obtained by the fishing activity with two types of harvesting policies, one based on variable effort, which is inapplicable, and the other based on a constant effort, which is applicable, sustainable and is socially advantageous. We use real data and consider a logistic and a Gompertz growth models to perform such comparisons. For both optimal policies, profitwise comparisons are also made when considering a logistic-type growth model with weak Allee effects. The mean and variance of the first passage times by a lower and by an upper thresholds are studied and, for a particular threshold value, we estimate the probability density function of the first passage time using the inversion of the Laplace transform; Resumo: MODELOS DE PESCA USANDO EQUAÇÕES DIFERENCIAIS ESTOCÁSTICAS: POLÍTICAS SUSTENTÁVEIS E OTIMIZAÇÃO DO LUCRO A dinâmica de crescimento de uma população sujeita a pesca em ambiente aleatório é descrita através de modelos de equações diferenciais estocásticas, onde o termo de captura depende de um esforço de pesca constante ou variável. Comparamos o lucro obtido pela atividade de pesca usando dois tipos de políticas de pesca, uma inaplicável e baseada em esforço variável e a outra aplicável, sustentável e socialmente vantajosa, baseada em esforço constante. As comparações são realizadas recorrendo a dados reais e considerando dois modelos de crescimento, o modelo logístico e o modelo de Gompertz. Para ambas as políticas ótimas, as comparações do lucro também são feitas quando se considera um modelo de crescimento do tipo logístico com efeitos de Allee fracos. A média e a variância dos tempos de primeira passagem por um limite inferior e por um limite superior são estudados e, para um determinado valor limite, estimamos a função de densidade do tempo de primeira passagem usando a inversa da transformada de Laplace