The impact of delivery risk on optimal production and futures hedging

Multiple delivery specifications exist on nearly all commodity futures contracts. Sellers are typically allowed to choose among several grades of the underlying commodity. On the delivery day, the futures price converges to the spot price of the cheapest-to-deliver grade rather than to that of the par-delivery grade of the commodity. This imposes an additional delivery risk on hedgers. This paper derives the optimal production and futures hedging strategy for a risk-averse competitive firm in the presence of delivery risk. We show that, depending on its relative valuation, the delivery option may induce the firm to produce more than in the absence of delivery risk. If delivery risk is additively related to commodity price risk, the firm will under-hedge its exposure to commodity price risk. If delivery risk is multiplicatively related to commodity price risk, the firm will under- or over-hedge this exposure. For constant relative risk aversion, this is illustrated by a numerical example.delivery risk, futures, risk management, production

Restricted Export Flexibility and Risk Management with Options and Futures

This paper examines the production, export and risk management decisions of a risk-averse competitive firm under exchange rate risk. The firm is export flexible in allocating its output to either the domestic market or a foreign market after observing the exchange rate. Export flexibility is restricted by certain minimum sales requirements that are due to long-term considerations. Currency options are sufficient to derive a separation result under restricted export flexibility. Under fairly priced currency futures and options, full hedging with both instruments is optimal. Introducing fairly-priced currency options stimulates production provided that the currency futures market is unbiased.restricted export flexibility, risk management, currency futures, currency options

Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming (Open Access publication)

An approach for optimising genetic contributions of candidates to control inbreeding in the offspring generation using semidefinite programming (SDP) was proposed. Formulations were done for maximising genetic gain while restricting inbreeding to a preset value and for minimising inbreeding without regard of gain. Adaptations to account for candidates with fixed contributions were also shown. Using small but traceable numerical examples, the SDP method was compared with an alternative based upon Lagrangian multipliers (RSRO). The SDP method always found the optimum solution that maximises genetic gain at any level of restriction imposed on inbreeding, unlike RSRO which failed to do so in several situations. For these situations, the expected gains from the solution obtained with RSRO were between 1.5–9% lower than those expected from the optimum solution found with SDP with assigned contributions varying widely. In conclusion SDP is a reliable and flexible method for solving contribution problems

Response to mass selection when an identified major gene is segregating

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Natural orbits of atomic Cooper pairs in a nonuniform Fermi gas

We examine the basic mode structure of atomic Cooper pairs in an inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasi-particle vacuum, the single particle density matrix and the anomalous density matrix share the same set of eigenfunctions. These eigenfunctions correspond to natural pairing orbits associated with the BCS ground state. We investigate these orbits for a Fermi gas in a spherical harmonic trap, and construct the wave function of a Cooper pair in the form of Schmidt decomposition. The issue of spatial quantum entanglement between constituent atoms in a pair is addressed.Comment: 14 pages, 4 figures, submitted to Phys. Rev.

Behaviour of the additive finite locus model

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Potential benefit from using an identified major gene in BLUP evaluation with truncation and optimal selection

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