Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

The radiation shielding offered by the commercial glass installed in Bangladeshi dwellings

One sign of a vibrant Bangladeshi economy has been the move away from the use of more traditional housing materials towards a preference for modern constructional media. Glass, one such example, used both decoratively and in a structural context, offers various advantageous properties and facets including a protective feature against radiation that has not previously been considered. Current interest examines the dosimetric possibilities offered by the commercial glass as a secondary shield and also in retrospective ionising radiation exposure analysis. Four popular brands of window glass are investigated, all available within the local market (PHP-Bangladesh, Usmania-Bangladesh, Nasir-Bangladesh and Rider-China), all with the same thickness and colour, varying in terms of elemental weight fractions as evaluated by energy dispersive X-ray analysis. As potential attenuators of transmitted radiation thereby forming secondary barriers against radiation exposure from penetrating radiations, the four brands of glass have been studied using photon energies from 59 up to 1332 keV, a range of values representative of that potentially encountered in incidents. Use has been made of a well-shielded high-purity germanium γ-ray spectrometer and associated electronics, providing for evaluation of the characteristic barrier parameters of half-value layer, radiation protection efficiency and effective atomic number (Z_eff). Of the four brands investigated, Rider provides superior secondary shielding performance. Concerning potential retrospective dosimetry the effective atomic number of the glass samples are comparable with that of the commercial thermoluminescence (TL) dosimeter TLD-200. At high doses, the TL yields are sufficient to provide for retrospective accident dosimetry.     

Stereochemistry-dependent, mechanoresponsive supramolecular host assemblies for fullerenes: a guest-induced enhancement of thixotropy

Self-assembly behaviors of a series of systems (G1, G2, and G3) possessing same organic building blocks based on a substituted anthracene have been investigated in decalin. G2 and G3 are dominated by head-to-tail (ht) and head-to-head (hh) type dimers of G1, respectively. G1 gives a thermoresponsive gel that behaves ideally, showing frequency-independent elastic and viscous moduli. Interestingly, G2 produces a thixotropic gel that shows the signature of structural relaxation, signifying the dynamic nature of the system. In contrast, G3 remains fluidlike. As investigated by scanning electron microscopy (SEM), in the assembly process of G2, first disklike nanoaggregates are formed, and in the second step these aggregates interact to construct the densely packed secondary assembly. A transition from secondary assembly to primary assembly under shear initiates the mechanoresponsive destruction of the gel. In the self-assembly process, G1 propagates in a one-dimensional fashion, whereas G2 and G3 can propagate in a two-dimensionional fashion. The same side orientation of the substituents in G3 facilitates the formation of a compact closed-shell-type structure, which results in the generation of isolated nanocrystals. The long-range weak interaction together with the capability of propagating in two dimensions is found to be essential for the construction of such a mechanoresponsive assembly. C(60) and C(70) could be incorporated successfully in G2 assembly to develop mechanoresponsive fullerene assemblies. The presence of fullerenes not only enhances the elastic properties of G2 but also intensifies the thixotropy. C(70) appears to be a superior guest in terms of property enhancement due to its better size fitting with the concave-shaped host.     

Cd(ii)-triggered excimer-monomer conversion of a pyrene derivative: time dependent red-shift of monomer emission with cell staining application

An efficient fluorescent probe (E)-N1-((E)-2-((pyren-7-yl)methyleneamino)ethyl)-N2-((pyren-7-yl)methylene)ethane-1,2-diamine (L) has been synthesized by a facile one-step condensation reaction. L can selectively detect Cd(2+) in presence of other common metal ions in 0.1 M HEPES buffered DMSO-water (4?:?1, v/v) medium. The detection limit of Cd(2+) is 1.8 × 10(-8) M. Cd(2+) can effectively convert the excimer emission of L into its monomer emission which in turn exhibits a time-dependent red-shift.     

Limiting Spectral Distribution of Random k-Circulants

Consider random k-circulants A _k,n with n????,k=k(n) and whose input sequence {a _l } _l??0 is independent with mean zero and variance one and $\sup_{n}n^{-1}\sum_{l=1}^{n}\mathbb{E}|a_{l}|^{2+\delta}<\infty$ for some ??>0. Under suitable restrictions on the sequence {k(n)} _n??1, we show that the limiting spectral distribution (LSD) of the empirical distribution of suitably scaled eigenvalues exists, and we identify the limits. In particular, we prove the following: Suppose g??1 is fixed and p ₁ is the smallest prime divisor of g. Suppose $P_{g}=\prod_{j=1}^{g}E_{j}$ where {E _j }_1??j??g are i.i.d. exponential random variables with mean one. (i) If k ^g =?1+sn where s=1 if g=1 and $s=o(n^{p_{1}-1})$ if g>1, then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{1}P_{g}^{1/(2g)}$ where U ₁ is uniformly distributed over the (2g)th roots of unity, independent of P _g . (ii) If g??2 and k ^g =1+sn with $s=o(n^{p_{1}-1})$ , then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{2}P_{g}^{1/(2g)}$ where U ₂ is uniformly distributed over the unit circle in ?², independent of P _g . On the other hand, if k??2, k=n ^o(1) with gcd?(n,k)=1, and the input is i.i.d. standard normal variables, then $F_{n^{-1/2}A_{k,n}}$ converges weakly in probability to the uniform distribution over the circle with center at (0,0) and radius $r=\exp(\mathbb{E}[\log\sqrt{E}_{1}])$ .     

Spectra of Large Random Trees

We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a principal submatrix of a Hermitian matrix and a suitable notion of local weak convergence for an ensemble of random trees that we call probability fringe convergence, we show that the empirical spectral distributions for many random tree models converge to a deterministic (model-dependent) limit as the number of vertices goes to infinity. Moreover, the masses assigned by the empirical spectral distributions to individual points also converge in distribution to constants. We conclude for ensembles such as the linear preferential attachment models, random recursive trees, and the uniform random trees that the limiting spectral distribution has a set of atoms that is dense in the real line. We obtain lower bounds on the mass assigned to zero by the empirical spectral measures via the connection between the number of zero eigenvalues of the adjacency matrix of a tree and the cardinality of a maximal matching on the tree. In particular, we employ a simplified version of an algorithm due to Karp and Sipser to construct maximal matchings and understand their properties. Moreover, we show that the total weight of a weighted matching is asymptotically equivalent to a constant multiple of the number of vertices when the edge weights are independent, identically distributed, nonnegative random variables with finite expected value, thereby significantly extending a result obtained by Aldous and Steele in the special case of uniform random trees. We greatly generalize a celebrated result obtained by Schwenk for the uniform random trees by showing that if any ensemble converges in the probability fringe sense and a very mild further condition holds, then, with probability converging to one, the spectrum of a realization is shared by at least one other (nonisomorphic) tree. For the linear preferential attachment model with parameter a>?1, we show that for any fixed k, the k largest eigenvalues jointly converge in distribution to a nontrivial limit when rescaled by $n^{1/2\gamma_{a}}$ , where ?? _a =a+2 is the Malthusian rate of growth parameter for an associated continuous-time branching process.     

Nonlinear fluorescence response driven by ATP-induced self-assembly of guanidinium-tethered tetraphenylethene

Nonlinear fluorescence response, which is particularly important to attain the high signal-to-background ratio, was realized by the aggregation-induced fluorescence increase of guanidinium-tethered tetraphenylethene with ATP.     

Average Cost Optimality for an Unreliable Two-Machine Flowshop with Limited Internal Buffer

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.