6 research outputs found
Search-Money-and-Barter Models of Financial Stabilization
A macroeconomic model based on search-theoretical foundations is built to show that in an economy with structural deficiencies of the Russian Virtual Economy, money substitutes appear as a result of optimizing behavior of agents. Moreover, the volume of money substitutes is typically large, and it is impossible to reduce their volume significantly by using standard instruments as an increase of the money supply or decreasing the tax level. The result obtains for an economy, where there are large natural monopolies and widespread informal networks.
Coherent States for Quantum Compact Groups
Coherent states are introduced and their properties are discussed for all
simple quantum compact groups. The multiplicative form of the canonical element
for the quantum double is used to introduce the holomorphic coordinates on a
general quantum dressing orbit and interpret the coherent state as a
holomorphic function on this orbit with values in the carrier Hilbert space of
an irreducible representation of the corresponding quantized enveloping
algebra. Using Gauss decomposition, the commutation relations for the
holomorphic coordinates on the dressing orbit are derived explicitly and given
in a compact R--matrix formulation (generalizing this way the --deformed
Grassmann and flag manifolds). The antiholomorphic realization of the
irreducible representations of a compact quantum group (the analogue of the
Borel--Weil construction) are described using the concept of coherent state.
The relation between representation theory and non--commutative differential
geometry is suggested.}Comment: 25 page
Categorical geometric skew Howe duality
We categorify the R-matrix isomorphism between tensor products of minuscule
representations of U_q(sl(n)) by constructing an equivalence between the
derived categories of coherent sheaves on the corresponding convolution
products in the affine Grassmannian. The main step in the construction is a
categorification of representations of U_q(sl(2)) which are related to
representations of U_q(sl(n)) by quantum skew Howe duality. The resulting
equivalence is part of the program of algebro-geometric categorification of
Reshitikhin-Turaev tangle invariants developed by the first two authors.Comment: 31 page
Predicting the time at which a Lévy process attains its ultimate supremum
We consider the problem of finding a stopping time that minimises the L 1-distance to θ, the time at which a Lévy process attains its ultimate supremum. This problem was studied in Du Toit and Peskir (Proc. Math. Control Theory Finance, pp. 95–112, 2008) for a Brownian motion with drift and a finite time horizon. We consider a general Lévy process and an infinite time horizon (only compound Poisson processes are excluded. Furthermore due to the infinite horizon the problem is interesting only when the Lévy process drifts to −∞). Existing results allow us to rewrite the problem as a classic optimal stopping problem, i.e. with an adapted payoff process. We show the following. If θ has infinite mean there exists no stopping time with a finite L 1-distance to θ, whereas if θ has finite mean it is either optimal to stop immediately or to stop when the process reflected in its supremum exceeds a positive level, depending on whether the median of the law of the ultimate supremum equals zero or is positive. Furthermore, pasting properties are derived. Finally, the result is made more explicit in terms of scale functions in the case when the Lévy process has no positive jumps