X dominates Y by FASD (SASD, TASD), denoted by X [[??].sub.1] Y or F [[??].sub.1] G (X [[??].sub.2]Y or F[[??].sub.2]G, X[[??].sub.3]Y or F[[??].sub.3]G) if and only if [F.sup.A.sub.1] (x) [less than or equal to] [G.sup.A.sub.1] (x) ([F.sup.A.sub.2] (x) [less than or equal to] [G.sup.A.sub.2] (x), [F.sup.A.sub.3] (x) [less than or equal to] [G.sup.A.sub.3] (x)) for all possible returns x, and the strict inequality holds in a nonempty interval.
Thus, risk-averse investors exhibit FASD (SASD, TASD) if their utility functions u belong to [U.sup.A.sub.1] ([U.sup.A.sub.2], [U.sup.A.sub.3]).
FASD implies SASD, which, in turn, implies TASD. However, the converse is not true: the existence of SASD does not imply the existence of FASD.
Hence, our finding implies that risk averters significantly prefer spot to futures in the sense of both SASD and TASD.
Here, FASD, SASD, and TASD (FDSD, SDSD, and TDSD) refer to first-, second-, and third-order ASD (DSD) for risk averters (risk seekers) defined in Definition 1 (2).
The implication is that risk averters significantly prefer spot to futures in the sense of both SASD and TASD in both subperiods.
A sentencing hearing at Newport Crown Court yesterday heard the theft came to light after Alexander, of Neath, was given a final written warning by TASDS managing director Daniel Hunt due to the way she spoke to members of the public and potential clients.
They carried out a full review of the company's accounts, which was hampered by Alexander's deletion of her emails, but they were able to identify accounts which matched with payments made by the TASDS account.
He said since leaving her job she had been declared bankrupt and had lost "everything" including the home she owned before joining TASDS.