All Regular-Solid Varieties of Idempotent Semirings

The lattice of all regular-solid varieties of semirings splits in two complete sublattices: the sublattice of all idempotent regular-solid varieties of semirings and the sublattice of all normal regular-solid varieties of semirings. In this paper, we discuss the idempotent part

All Linear-Solid Varieties of Semirings

A variety of semirings is said to be solid if each of its identities is satisfied as hyperidentity. There are precisely four solid varieties of semirings. Each of them contains every derived algebra, where the both fundamental operations are replaced by arbitrary binary term operations. If a variety contains all linear derived algebras, where the fundamental operations are replaced by term operations induced by linear terms, it is called linear-solid. We prove that a variety of semirings is solid if and only if it is linear-solid

Index options : a model-free approach

This paper contains an overview and an extension of the theory on comonotonicity-based model-free upper bounds and super-replicating strategies for stock index options, as presented in Hobson et al. (2005) and Chen et al. (2008). Whereas these authors only consider index call options, here a unified approach for call and put options is presented. Considering a unified framework gives rise to an e¢ cient algorithm for calculating upper bounds and for determining the corresponding superhedging strategies for both cases. The unified framework also allows to extend several existing results, in particular on the optimality of the superhedging strategies. Several practical issues concerning the implementation of the results are discussed. In particular, a simplified algorithm is presented for the situation where for some of the constituent stock in the index there are no options available