Optimization problems with quasiconvex inequality constraints

The constrained optimization problem min f(x), gj(x) 0 (j = 1, . . . , p) is considered, where f : X ! R and gj : X ! R are nonsmooth functions with domain X Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of the Dini derivative; to obtain more sensitive conditions, it admits directionally dependent multipliers. The two cases, where the Lagrange function satisfies a non-strict and a strict inequality, are considered. In the case of a non-strict inequality pseudoconvex functions are involved and in their terms some properties of the convex programming problems are generalized. The efficiency of the obtained conditions is illustrated on an example. Key words: Nonsmooth optimization, Dini directional derivatives, quasiconvex functions, pseudoconvex functions, quasiconvex programming, Kuhn-Tucker conditions.

Bond Immunization and Exchange Rate Risk: Some Further Considerations

This research project seeks to address two critical problems in the theory of international bond pricing: 1) how can exchange rate risk be formally incorporated into standard bond valuation models?, and 2) how must strategies to “immunize†bonds against interest rate and inflation risk be modified to also incorporate exchange rate risk? Most of all, this study analyzes the mathematical properties of international bonds (e.g., Eurobonds). A special consideration is given to the two most important characteristics of debt securities – duration and convexity and through them to the various ways to immunize bonds and bond portfolios from real interest, inflation, and exchange rate risks. Fogler (1984) formally addressed the effects of changes in inflation and interest rates on bond prices. Unfortunately, exchange rate risk does not appear to have been formally incorporated into these previous models. Moreover, we correct a mathematical error in Fogler’s analysis.bond immunization

The twistor space of a quaternionic contact manifold

We show that the CR structure on the twistor space of a quaternionic contact structure described by Biquard is normal if and only if the Ricci curvature of the Biquard connection commutes with the endomorphisms in the quaternionic structure of the contact distribution.Comment: 15pages, LaTeX2e, typos corrected, final version to appear in Quart. J. Math. (Oxford

Fermionic full counting statistics with smooth boundaries: from discrete particles to bosonization

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher--Hartwig expansion for Toeplitz determinants, while in the continuous limit we recover the bosonization results. This example of full counting statistics with smoothing is also related to orthogonality catastrophe, Fermi-edge singularity and non-equilibrium bosonization.Comment: 7 pages, 4 figure