基于辐射声功率最小化的安静结构设计

本文研究了一种基于模型修改使结构辐射声功率最小的方法，使用了结构动力学、声学和优化理论等学科知识，对结构修改后固有频率变化可以忽略不计时的声辐射优化进行了研究，将设计变量看作外部阻抗，对结构的表面振速进行了重新分布，可以降低结构辐射的声功率。将质量块与动力吸振器进行组合实现声辐射最小化，不但降低了一定频率范围内的平均声功率，还降低了动力吸振器所对应的单频下的声功率；运用遗传算法搜索结构辐射声功率最小时附加质量块或动力吸振器的位置，对附加质量块和有源控制作用下简支钢板的声功率最小化进行了比较研究，阐明了附加外部结构与有源控制实现安静结构的物理机理。最后，对本文提出的基于平板辐射声功率最小化的安静结构设计方法进行了实验验证。     

An Affine Scaling Interior Trust Region Method via Optimal Path for Solving Monotone Variational Inequality Problem with Linear Constraints

Based on a differentiable merit function proposed by Taji et al. in ＂Math. Prog. Stud., 58, 1993, 369-383＂, the authors propose an affine scaling interior trust region strategy via optimal path to modify Newton method for the strictly monotone variational inequality problem subject to linear equality and inequality constraints. By using the eigensystem decomposition and affine scaling mapping, the authors form an affine scaling optimal curvilinear path very easily in order to approximately solve the trust region subproblem. Theoretical analysis is given which shows that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions.     

Multiscale asymptotic method of optimal control on the boundary for heat equations of composite materials

In this paper, we study the optimal control on the boundary for parabolic equations with rapidly oscillating coefficients arising from the heat transfer problems and the optimal control on the boundary of composite materials or porous media. The multiscale asymptotic expansion of the solution for the problem in the case without any constraints is presented. We derive the proofs of all convergence results.     

Variational Inequalities for Leavable Bounded-Velocity Control

We study the variational inequality associated with a bounded-velocity control problem when discretionary stopping is allowed. We establish the existence of a strong solution by using the viscosity solution techniques. The optimal policy is shown to exist from the optimality conditions in the variational inequality.     

Optimal hedging strategies for multi-period guarantees in the presence of transaction costs: A stochastic programming approach

Multi-period guarantees are often embedded in life insurance contracts. In this paper we consider the problem of hedging these multi-period guarantees in the presence of transaction costs. We derive the hedging strategies for the cheapest hedge portfolio for a multi-period guarantee that with certainty makes the insurance company able to meet the obligations from the insurance policies it has issued. We find that by imposing transaction costs, the insurance company reduces the rebalancing of the hedge portfolio. The cost of establishing the hedge portfolio also increases as the transaction cost increases. For the multi-period guarantee there is a rather large rebalancing of the hedge portfolio as we go from one period to the next. By introducing transaction costs we find the size of this rebalancing to be reduced. Transaction costs may therefore be one possible explanation for why we do not see the insurance companies performing a large rebalancing of their investment portfolio at the end of each year.     

The pricing and optimal strategies of callable warrants

In this paper, we introduce a valuation model of callable warrants under a setting of the optimal stopping problem between the holder (investor) and the issuer (firm). A warrant is the right to purchase new shares at a predetermined price. When the new stocks are issued, the value of the stock is diluted. We consider the model taking the dilution into account. After identifying optimal policies for the issuer and the investor, we explore the analytical properties of the optimal exercise and call boundaries for the holder and the issuer, respectively. Furthermore, the value of such a callable warrant and the optimal critical prices are examined numerically using the binomial method.     

Callable risky perpetual debt with protection period

Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection (‘grace’) period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of perpetual debt and barrier options with a time dependent barrier. We also analyze how an issuer’s optimal bankruptcy decision is affected by the existence of the call option by using closed-form approximations. The model quantifies the increased coupon and the decreased initial bankruptcy level caused by the embedded option. Examples indicate that our closed form model produces reasonably precise coupon rates compared to numerical solutions. The credit-spread produced by our model is in a realistic order of magnitude compared to market data.     

Symmetry reductions and exact solutions of the affine heat equation

Lie symmetry group method is applied to study the affine heat equation for surface. Its symmetry groups and corresponding optimal systems are determined, and group-invariant solutions associated to the symmetries are obtained and classified.     

Optimal threshold analysis of segmentation methods for identifying target customers

In CRM (Customer Relationship Management), the importance of a segmentation method for identifying good customers has been increasing. For evaluation of different segmentation methods, Accuracy often plays a key role. This indicator, however, cannot distinguish two types of errors. The purpose of this paper is to overcome this pitfall by introducing two different indicators: Recall and Precision. Assuming that a promotion is addressed exclusively to the selected target customers, the financial effectiveness of the underlying segmentation method is expressed as a function of Recall and Precision. An optimization problem is then formulated so as to maximize the financial measure by finding the optimal threshold level in terms of the severeness for estimating the target set. By introducing a functional form which represents correctness and mistakes about the target set, the unique optimal solution is derived explicitly. The proposed approach is validated by using real customer purchase data.     

Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation

We present an exactly soluble optimal stochastic control problem involving a diffusive two-states random evolution process and connect it to a nonlinear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between the non-linear Boltzmann-like equations introduced by Ruijgrok and Wu and the optimal control of a two-states random evolution process. In the sense of this generalization, the nonlinear reaction-diffusion equation is identified as the natural diffusive generalization of the Ruijgrok–Wu and Boltzmann model.