Exact Simulation Problems for Jump-Diffusions

Exact simulation of SDEs is a very important and challenging problem. In this paper we discuss exact simulation problems for jump-diffusion processes. Motivated by statistical applications, our main contribution is to propose an algorithm that performs exact simulation of a class of jump-diffusion bridges. We also present and discuss the existing methods for forward simulation and propose an extension of one of them to account for unbounded jump rate. Finally, the exact algorithms are compared to competing non-exact ones in some simulated examples.     

Goal achieving probabilities of cone‐constrained mean‐variance portfolios

In this paper, we establish closed‐form formulas for key probabilistic properties of the cone‐constrained optimal mean‐variance strategy, in a continuous market model driven by a multidimensional Brownian motion and deterministic coefficients. In particular, we compute the probability to obtain to a point, during the investment horizon, where the accumulated wealth is large enough to be fully reinvested in the money market, and safely grow there to meet the investor's financial goal at terminal time. We conclude that the result of Li and Zhou [Ann. Appl. Prob., v.16, pp.1751–1763, (2006)] in the unconstrained case carries over when conic constraints are present: the former probability is lower bounded by 80% no matter the market coefficients, trading constraints, and investment goal. We also compute the expected terminal wealth given that the investor's goal is underachieved, for both the mean‐variance strategy and the aforementioned hybrid strategy where transfer to the money market occurs if it allows to safely achieve the goal. The former probabilities and expectations are also provided in the case where all risky assets held are liquidated if financial distress is encountered. These results provide investors with novel practical tools to support portfolio decision‐making and analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

In this paper, the boundedness of a large class of sublinear commutator operators T _b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class A _p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ ₁, φ ₂) which ensure the boundedness of the operator T _b from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of T _b are given in terms of Zygmund-type integral inequalities on (φ ₁, φ ₂), which do not require any assumption on monotonicity of φ ₁(x, r), φ ₂(x, r) in r. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.     

The number of topological generators for full groups of ergodic equivalence relations

We completely elucidate the relationship between two invariants associated with an ergodic probability measure-preserving (pmp) equivalence relation, namely its cost and the minimal number of topological generators of its full group. It follows that for any free pmp ergodic action of the free group on \(n\) generators, the minimal number of topological generators for the full group of the action is \(n+1\) , answering a question of Kechris.     

A continuous characterization of the maximum-edge biclique problem

The problem of finding large complete subgraphs in bipartite graphs (that is, bicliques) is a well-known combinatorial optimization problem referred to as the maximum-edge biclique problem (MBP), and has many applications, e.g., in web community discovery, biological data analysis and text mining. In this paper, we present a new continuous characterization for MBP. Given a bipartite graph $G$ , we are able to formulate a continuous optimization problem (namely, an approximate rank-one matrix factorization problem with nonnegativity constraints, R1N for short), and show that there is a one-to-one correspondence between (1) the maximum (i.e., the largest) bicliques of $G$ and the global minima of R1N, and (2) the maximal bicliques of $G$ (i.e., bicliques not contained in any larger biclique) and the local minima of R1N. We also show that any stationary points of R1N must be close to a biclique of $G$ . This allows us to design a new type of biclique finding algorithm based on the application of a block-coordinate descent scheme to R1N. We show that this algorithm, whose algorithmic complexity per iteration is proportional to the number of edges in the graph, is guaranteed to converge to a biclique and that it performs competitively with existing methods on random graphs and text mining datasets. Finally, we show how R1N is closely related to the Motzkin–Strauss formalism for cliques.     

Scale-up synthesis of zinc borate from the reaction of zinc oxide and boric acid in aqueous medium

Synthesis of zinc borate was conducted in a laboratory and a pilot scale batch reactor to see the influence of process variables on the reaction parameters and the final product, 2ZnO·3B₂O₃·3.5H₂O. Effects of stirring speed, presence of baffles, amount of seed, particle size and purity of zinc oxide, and mole ratio of H₃BO₃:ZnO on the zinc borate formation reaction were examined at a constant temperature of 85 °C in a laboratory (4 L) and a pilot scale (85 L) reactor. Products obtained from the reaction in both reactors were characterized by chemical analysis, X-ray diffraction, particle size distribution analysis, thermal gravimetric analysis and scanning electron microscopy. The kinetic data for the zinc borate production reaction was fit by using the logistic model. The results revealed that the specific reaction rate, a model parameter, decreases with increase in particle size of zinc oxide and the presence of baffles, but increases with increase in stirring speed and purity of zinc oxide; however, it is unaffected with the changes in the amount of seed and reactants ratio. The reaction completion time is unaffected by scaling-up.     

s-process stellar enhancement factors obtained within the statistical model with parity-dependent level densities

In stellar environments the medium modifications of the neutron capture cross-sections required for s-process nucleosynthesis simulations are accounted for by the stellar enhancement factors. We have calculated these enhancement factors using the statistical model for compound reactions. Improving previous calculations we take the parity distribution of states at all stages of the reaction into account by using parity-dependent level densities. The effect of this improvement on the stellar enhancement factors is small, although not negligible if one attempts to describe the stellar capture rates with an accuracy of order 10%. We observe, however, that the uncertainties introduced by the insufficient knowledge of the total level densities are noticeably larger.     

A taylor collocation method for solving high‐order linear pantograph equations with linear functional argument

A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011     

Study of zinc hexacyanoferrate—modified platinum electrodes using electrochemical quartz crystal microbalance

In this work, the electrochemical quartz crystal microbalance has been employed to monitor directly the in situ growth of the zinc hexacyanoferrate film during the electrodeposition. Mass changes of the platinum|crystal working electrode were correlated with cyclic voltammetry data. Effects of the sorption of counter-cations (K⁺, Na⁺, and NH₄⁺ {\hbox{NH}}_4^{+} and anions (Cl⁻ and SO₄^{2 -} {\hbox{SO}}_4^{2 - } ) during redox reactions were studied. The electrocatalytic oxidation properties of procaine by the zinc hexacyanoferrate films were performed.