Learning from outside the viability kernel: Why we should build robots that can fall with grace

<p>Sustainability in fisheries is a complex concept and one that has attracted a rich history of research over time. The basic concerns of sustainability are how to reconcile ecological, economic and social requirements within the perspectives of intra- and inter-generational equity. Therefore, maintaining these requirements simultaneously is critical to achieving a perennial system and avoiding so-called “crisis” situations. It is contended that viability theory, which is a relatively new area of mathematics, rigorously captures the essence of sustainability. Using viability theory, this thesis develops two viability models based on different direct conservation measures (i.e. input and output controls) to examine the feasibility conditions under which a regulator can achieve sustainability in a fishery characterised by a “by-catch process”, whereby one species is targeted and another species is incidentally caught as by-catch. The first model considers a by-catch fishery where fishing input is controlled by a regulator. The second model considers two interrelated fisheries managed using a dual quantity-price system, which is based on New Zealand’s Quota Management System (QMS). For each model, the set of constraints representing the “good health” of the system are characterised using managerial priorities identified in the literature. Then, the viability kernel, which is the largest set of initial states for which there are controls that result in inter-temporal trajectories satisfying all the constraints, is approximated numerically. This is achieved by employing VIKAASA, which is a computer application capable of generating kernel approximations. The viability kernel provides the regulator with meaningful reference values and indicators for desirable or undesirable states of the fishery, which serve as important inputs into policy decisions. This study also shows the potential for viability theory to provide policy makers with a better insight of how to integrate ecosystem considerations into the QMS.</p>

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The calculation of discriminating kernel based on viability kernel and reachability

Advances in Difference Equations ◽

10.1186/s13662-017-1429-2 ◽

2017 ◽

Vol 2017 (1) ◽

Cited By ~ 2

Author(s):

Yanli Han ◽

Yan Gao

Keyword(s):

Viability Kernel ◽

Discriminating Kernel

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VIABLE CAPTURE BASIN FOR STUDYING DIFFERENTIAL AND HYBRID GAMES: APPLICATION TO FINANCE

International Game Theory Review ◽

10.1142/s0219198904000101 ◽

2004 ◽

Vol 06 (01) ◽

pp. 109-136 ◽

Cited By ~ 12

Author(s):

PATRICK SAINT-PIERRE

Keyword(s):

Control Problem ◽

Stochastic Control ◽

Control Problems ◽

Viability Theory ◽

Viability Kernel ◽

Stochastic Viability ◽

Guaranteed Control ◽

Recent Developments ◽

The One ◽

Dynamical Game

Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability/capturability algorithm evaluates and manages portfolios. Regarding viability/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox–Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus.

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