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On the Impact of Biological Risk in Aquaculture Valuation and Decision Making

Christian-Oliver Ewald, Kevin Kamm

Abstract

This paper explores the impact of stochastic mortality and disease on animal-based commodities, with a specific emphasis on aquaculture, particularly in the context of salmon farming. The investigation delves into the stochastic nature of mortality and treatment plans based on historical data related to salmon lice. Given that salmon lice pose a significant challenge in salmon farming, with associated treatment costs estimated to be comparable to feeding expenses, their removal is imperative to ensure the survival of the salmon and comply with the Norwegian government's stipulation of maintaining 0.5 lice per fish. We propose a new model that considers the relationship between hosts and parasites to estimate the number of treatments required and their overall cost. An important aspect of this model is its incorporation of stochastic effectiveness for each removal. After calibrating the model to the available data, the study examines the stochastic behavior's impact on the optimal harvesting decision in comparison to deterministic mortality models. The results indicate an approximate $1.5\,\%$ increase in the value of the salmon farm when employing the harvesting rule based on the stochastic host-parasite model as opposed to a deterministic model.

On the Impact of Biological Risk in Aquaculture Valuation and Decision Making

Abstract

This paper explores the impact of stochastic mortality and disease on animal-based commodities, with a specific emphasis on aquaculture, particularly in the context of salmon farming. The investigation delves into the stochastic nature of mortality and treatment plans based on historical data related to salmon lice. Given that salmon lice pose a significant challenge in salmon farming, with associated treatment costs estimated to be comparable to feeding expenses, their removal is imperative to ensure the survival of the salmon and comply with the Norwegian government's stipulation of maintaining 0.5 lice per fish. We propose a new model that considers the relationship between hosts and parasites to estimate the number of treatments required and their overall cost. An important aspect of this model is its incorporation of stochastic effectiveness for each removal. After calibrating the model to the available data, the study examines the stochastic behavior's impact on the optimal harvesting decision in comparison to deterministic mortality models. The results indicate an approximate increase in the value of the salmon farm when employing the harvesting rule based on the stochastic host-parasite model as opposed to a deterministic model.
Paper Structure (14 sections, 19 equations, 6 figures, 2 tables)

This paper contains 14 sections, 19 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature review.
  3. Mathematical and Model Framework
  4. Salmon Farm Parameters
  5. Stochastic Mortality and Treatment Costs
  6. Treatment costs.
  7. Feeding and Harvesting Costs
  8. Optimal Stopping Problem
  9. Numerical Experiments
  10. Future Market Data
  11. Lice and Treatment Data
  12. Calibration of the Host-Parasite Model
  13. Comparison of Exercise Decisions
  14. Conclusion and Limitations

Figures (6)

  • Figure 1: Evolution of treatment techniques in Trø ndelag from 2012 till today.
  • Figure 2: Evolution of lice per fish, as well as countermeasures for one specific salmon farm from 2012 till today.
  • Figure 3: Evolution of lice per fish till first mechanical removal for farms in Trø ndelag, excluding all periods with additional treatments to mechanical removals.
  • Figure 4: Evolution of distributions of cumulative mechanical removals for farms in Trø ndelag, excluding all periods with additional treatments to mechanical removals.
  • Figure 5: One trajectory of the simulated host model with treatments (bold red line) and corresponding lice per fish in blue dots.
  • ...and 1 more figures