An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve

This paper presents a model for optimally designing a collateralized mortgage obligation (CMO) with a planned amortization class (PAC)-companion structure using dynamic cash reserve. In this structure, the mortgage pool’s cash flow is allocated by rule to the two bond classes such that PAC bondholders receive substantial prepayment protection, that protection being provided by the companion bondholders. The structure we propose provides greater protection to the PAC bondholders than current structures during periods of rising interest rates when this class of bondholders faces greater extension risk. We do so by allowing a portion of the cash flow from the collateral to be reserved to meet the PAC’s scheduled cash flow in subsequent periods. The greater protection is provided by the companion bondholders exposure to interest loss. To tackle this problem, we transform the problem of designing the optimal PAC-companion structure into a standard stochastic linear programming problem which can be solved efficiently. Moreover, we present an extended model by considering the quality of the companion bond and by relaxing the PAC bondholder shortfall constraint. Based on numerical experiments through Monte Carlo simulation, we show the utility of the proposed model.     

A parallel inexact newton method for stochastic programs with recourse

A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear convergence of the method are established. Furthermore, the method provides an error estimate which does not require much extra computation. The performance of the method is illustrated on a CM5 parallel computer.This work was supported by the Australian Research Council and the numerical experiments were done on the Sydney Regional Centre for Parallel Computing CM5.     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

Fluorescent humic substances–arsenic complex in well water in areas where blackfoot disease is endemic in Taiwan

The relationship between the four components, (1) fluorescence intensity, (2) arsenic concentration, (3) pH and (4) total dissolved solids, (TDS) measured in well waters from areas in Taiwan where blackfoot disease (BFD) is endemic was studied, as well as the relationships between the four degrees of BFD and each of the above four symptomatic components, in order to evaluate the etiological factors of BFD more progressively. The following 95% confidence intervals were obtained in well water samples (n = 1189): fluorescence intensity, 26.837–32.570; arsenic concentration, 0.103–0.127 mg dm^?3; pH, 7.466–7.519; and TDS 733.063–801.647 mg dm^?3. Fluorescence intensities of the four degrees of BFD were not all the same (F = 64.54, P < 0.001), and nor were arsenic concentrations (F = 72.03, P < 0.001), pH values (F = 7.30, P < 0.001), nor TDS values (F = 10.76, P < 0.001). In addition, multiple comparisons indicate that the higher the epidemical degree, the higher the fluorescence intensities, arsenic concentrations and pH values become; however, such a relationship is not found for TDS values. Moreover, the fluorescence intensities have positive linear correlations with arsenic concentrations (r = 0.49, P < 0.001), pH (r = 0.25, P < 0.001), and TDS (r = 0.18, P < 0.001), as do the arsenic concentrations with pH (r = 0.22, P < 0.001). Of the four epidemical degree groups, pairs are not significantly different from one another in correlation coefficients between fluorescence intensity and arsenic concentration, which implies a steady relationship between fluorescent compounds and arsenic. We conclude that fluorescent compounds in well water, as possible etiological factors of BFD, are closely related to arsenic along with pH and TDS values in the areas where BFD is endemic. In addition, we infer that a complex is formed by fluorescent compounds, arsenic and other metals.     

在相干理论的基础上分析光栅成像

本文在相干理论的基础上,推导了光栅成像中的光强分布和物像位置关系,并给出一组具有不同参数的实验照片及一组借助计算机绘制的强度分布图。     

New efficient numerical procedures for solving stochastic variational problems with a priori maximum pointwise error estimates

In a previous paper we gave a new formulation and derived the Euler equations and other necessary conditions to solve strong, pathwise, stochastic variational problems with trajectories driven by Brownian motion. Thus, unlike current methods which minimize the control over deterministic functionals (the expected value), we find the control which gives the critical point solution of random functionals of a Brownian path and then, if we choose, find the expected value.This increase in information is balanced by the fact that our methods are anticipative while current methods are not. However, our methods are more directly connected to the theory and meaningful examples of deterministic variational theory and provide better means of solution for free and constrained problems. In addition, examples indicate that there are methods to obtain nonanticipative solutions from our equations although the anticipative optimal cost function has smaller expected value.In this paper we give new, efficient numerical methods to find the solution of these problems in the quadratic case. Of interest is that our numerical solution has a maximal, a priori, pointwise error of O(h3/2) where h is the node size. We believe our results are unique for any theory of stochastic control and that our methods of proof involve new and sophisticated ideas for strong solutions which extend previous deterministic results by the first author where the error was O(h²).We note that, although our solutions are given in terms of stochastic differential equations, we are not using the now standard numerical methods for stochastic differential equations. Instead we find an approximation to the critical point solution of the variational problem using relations derived from setting to zero the directional derivative of the cost functional in the direction of simple test functions.Our results are even more significant than they first appear because we can reformulate stochastic control problems or constrained calculus of variations problems in the unconstrained, stochastic calculus of variations formulation of this paper. This will allow us to find efficient and accurate numerical solutions for general constrained, stochastic optimization problems. This is not yet being done, even in the deterministic case, except by the first author.     

A new formula for the saddle-to-scission time

We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very heavy nuclei.     

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.     

Coordinating inventory control and pricing strategies: The continuous review model

We analyze an infinite horizon, single product, continuous review model in which pricing and inventory decisions are made simultaneously and ordering cost includes a fixed cost. We show that there exists a stationary (s,S) inventory policy maximizing the expected discounted or expected average profit under general conditions.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.