It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work it was shown that when invoked as a fundamental first...

We investigate the generalisations of the Quispel, Roberts and Thompson (QRT) family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables. We assume invariance of the rational expression under a cyclic permutation of variables and we impose a...

Optimal control problem is considered: endogenous variables are to track some reference (targent) values. Uncertainty about future values of optimal targents may occur, so some pieces of information, about their characteristics may be very helpfu1. It will be shown, that certainty equivalence...

We generalize the concept of symplectic maps to that of k- symplectic maps: maps whose kth iterates are symplectic. Similarly, k-symmetries and k-integrals are symmetries (resp. integrals) of the kth iterate of the map. It is shown that k-symmetries and k-integrals are related by the...

Let Xt be a discrete multivariate autoregressive process of order 1. The paper derives the joint moment generating function (mgf) of the two quadratic forms that are used to define statistics relating to the parameters of this process. The formula is then specialized to some cases of interest,...