Cross sectional efficient estimation of stochastic volatility short rate models

We consider the problem of estimation of term structure of interest rates. Filtering theory approach is very natural here with the underlying setup being non-linear and non-Gaussian. Earlier works make use of Extended Kalman Filter (EKF). However, the EKF in this situation leads to inconsistent estimation of parameters, though without high bias. One way to avoid this is to use methods like Efficient Method of Moments or Indirect Inference Method. These methods, however, are numerically very demanding. We use Kitagawa type scheme for nonlinear filtering problem, which solves the inconsistency problem without being numerically so demanding. \u

On solving discrete optimization problems with one random element under general regret functions

In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and define an optimal solution as one having the least possible risk. We show that for discrete optimization problems with one random element and with min-sum objective functions a least risk solution for the stochastic problem can be obtained by solving a non-stochastic counterpart where the latter is constructed by replacing the random element of the former with a suitable parameter. We show that the above surrogate is the mean if the stochastic problem has only one symmetrically distributed random element. We obtain bounds for this parameter for certain classes of asymmetric distributions and study the limiting behavior of this parameter in details under two asymptotic frameworks. \u

On solving discrete optimization problems with multiple random elements under general regret functions

In this paper we attempt to find least risk solutions for stochastic discrete optimization problems (SDOP) with multiple random elements, where the feasibility of a solution does not depend on the particular values the random elements in the problem take. While the optimal solution, for a linear regret function, can be obtained by solving an auxiliary (non-stochastic) discrete optimization problem (DOP), the situation is complex under general regret. We characterize a finite number of solutions which will include the optimal solution. We establish through various examples that the results from Ghosh, Mandal and Das (2005) can be extended only partially for SDOPs with additional characteristics. We present a result where in selected cases, a complex SDOP may be decomposed into simpler ones facilitating the job of finding an optimal solution to the complex problem. We also propose numerical local search algorithms for obtaining an optimal solution. \u

Vortex dynamics and second magnetization peak in PrFeAsO0.60_{0.60}F0.12_{0.12} superconductor

We have studied the vortex dynamics in the PrFeAsO$_{0.60}$F$_{0.12}$ superconducting sample by dc magnetization and dynamic magnetization-relaxation rate $(Q)$ measurements. The field dependence of the superconducting irreversible magnetization $M_s$ reveals a second magnetization peak or fishtail effect. The large value of $Q$ is an indication of moderate vortex motion and relatively weak pinning energy. Data analysis based on the generalized inversion scheme suggests that the vortex dynamics can be described by the collective pinning model. The temperature dependence of the critical current is consistent with the pinning due to the spatial variation in the mean free path near a lattice defect ($\delta l$ pinning). The temperature and field dependence of $Q$ indicates a crossover from elastic to plastic vortex creep with increasing temperature and magnetic field. Finally, we have constructed the vortex phase diagram based on the present data.Comment: 11 pages, 8 Figures, Accepted for publication in Journal of Applied Physic

A Number of Quasi-Exactly Solvable N-body Problems

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set and many of their properties are similar to those of the Bender-Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.Comment: 17pages, Revtex, no figur