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This paper is concerned with the valuation of options in jump diffusion models. The partial integro-differential equation (PIDE) inherent in the pricing problem is solved by using the Mellin integral transform. The solution is a single integral expression independent of the distribution of the jump size. We also derive analytical expressions for the Greeks. The results are implemented and compared to other approaches.
Seafood plays an important role in human nutrition and its increased consumption is actively recommended for sustenance and health benefits in both developing and developed countries. In parallel to this, the public receives confusing advice as to what seafood is sustainably produced and is frequently misled about the environmental impacts of fishing, especially in locations such as Australia where contemporary fishery management has a conservation and sustainability focus. It is recognised globally that Australia’s traditional fishery management driven by strict sustainability and biodiversity regulations, has achieved impressive results in managing both fish stocks and the effects of fishing on marine environments. Despite this, continued pressure from non-government organisations (NGOs) and a perpetuation of the misuse of management terms such as “overfished” is used to promote the misguided need for ever increasing fishing restrictions, most obviously in “protected areas”. This paper questions the motives of some NGOs and governments in Australia in pursuing additional restrictions on fishing which are mostly unnecessary and disproportionate to the sustainability requirements of other sources of food. This is done within the context of the global need for sustainable seafood supply and the need for effective marine conservation that addresses all threats to marine ecosystems in proportion to the magnitude of each threat.