CAPM and Option Pricing with Elliptical Disbributions

In this paper, we offer an alternative proof of the Capital Asset Pricing Model when the returns follow a multivariate elliptical distribution. Empirical studies continue to demonstrate the inappropriateness of the normality assumption in modelling asset returns. The class of elliptical distributions,which includes the more familiar Normal distribution, provides flexibility in modelling the thickness of tails associated with the possibility that asset returns take extreme values with non-negligible probabilities. Within this framework, we prove a new version of Stein's lemma for elliptical distribution and use this result to derive the CAPM when returns are elliptical. We also derive a closed form solution of call option prices when the underlying is elliptically distributed. We use the probability distortion function approach based on the dual utility theory of choice under uncertainty.

Novel CCII-based Field Programmable Analog Array and its Application to a Sixth-Order Butterworth LPF

In this paper, a field programmable analog array (FPAA) is proposed. The proposed FPAA consists of seven configurable analog blocks (CABs) arranged in a hexagonal lattice such that the CABs are directly connected to each other. This structure improves the overall frequency response of the chip by decreasing the parasitic capacitances in the signal path. The CABS of the FPAA is based on a novel fully differential digitally programmable current conveyor (DPCCII). The programmability of the DPCCII is achieved using digitally controlled three-bit MOS ladder current division network. No extra biasing circuit is required to generate specific analog control voltage signals. The DPCCII has constant standby power consumption, offset voltage, bandwidth and harmonic distortions over all its programming range. A sixth-order Butterworth tunable LPF suitable for WLAN/WiMAX receivers is realized on the proposed FPAA. The filter power consumption is 5.4mW from 1V supply; it’s cutoff frequency is tuned from 5.2 MHz to 16.9 MHz. All the circuits are realized using 90nm CMOS technology from TSMC. All simulations are carried out using Cadence

Analysis of Quickselect under Yaroslavskiy's Dual-Pivoting Algorithm

There is excitement within the algorithms community about a new partitioning method introduced by Yaroslavskiy. This algorithm renders Quicksort slightly faster than the case when it runs under classic partitioning methods. We show that this improved performance in Quicksort is not sustained in Quickselect; a variant of Quicksort for finding order statistics. We investigate the number of comparisons made by Quickselect to find a key with a randomly selected rank under Yaroslavskiy's algorithm. This grand averaging is a smoothing operator over all individual distributions for specific fixed order statistics. We give the exact grand average. The grand distribution of the number of comparison (when suitably scaled) is given as the fixed-point solution of a distributional equation of a contraction in the Zolotarev metric space. Our investigation shows that Quickselect under older partitioning methods slightly outperforms Quickselect under Yaroslavskiy's algorithm, for an order statistic of a random rank. Similar results are obtained for extremal order statistics, where again we find the exact average, and the distribution for the number of comparisons (when suitably scaled). Both limiting distributions are of perpetuities (a sum of products of independent mixed continuous random variables).Comment: full version with appendices; otherwise identical to Algorithmica versio

Topological phases of topological insulator thin films

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi$_2$Se$_3$ and Bi$_2$Te$_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi$_2$Se$_3$, making Bi$_{2}$Te$_{3}$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators

Proximity-induced topological phases in bilayer graphene

We study the band structure of phases induced by depositing bilayer graphene on a transition metal dichalcogenide monolayer. Tight-binding and low-energy effective Hamiltonian calculations show that it is possible to induce topologically nontrivial phases that should exhibit spin Hall effect in these systems. We classify bulk insulating phases through calculation of the Z$_2$ invariant, which unequivocally identifies the topology of the structure. The study of these and similar hybrid systems under applied gate voltage opens the possibility for tunable topological structures in real experimental systems.Comment: 4 pages, 4 figure

Proximity-Induced Superconductivity at Non-Helical Topological Insulator Interfaces

We study how non-helical spin textures at the boundary between a topological insulator (TI) and a superconductor (SC) affect the proximity-induced superconductivity of the TI interface state. We consider TIs coupled to both spin-singlet and spin-triplet SCs, and show that for the spin-triplet parent SCs the resulting order parameter induced onto the interface state sensitively depends on the symmetries which are broken at the TI-SC boundary. For chiral spin-triplet parent SCs, we find that nodal proximity-induced superconductivity emerges when there is broken twofold rotational symmetry which forces the spins of the non-helical topological states to tilt away from the interface plane. We furthermore show that the Andreev conductance of lateral heterostructures joining TI-vacuum and TI-SC interfaces yields experimental signatures of the reduced symmetries of the interface states.Comment: 5 pages, 2 figure