相关论文: Numerical Solution of a parabolic problem arising …

In this paper, we use replica analysis to determine the investment strategy that can maximize the net present value for portfolios containing multiple development projects. Replica analysis was developed in statistical mechanical…

We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability…

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear…

We propose an approach to applying neural networks on linear parabolic variational inequalities. We use loss functions that directly incorporate the variational inequality on the whole domain to bypass the need to determine the stopping…

We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…

In the context of investment analysis, we formulate an abstract online computing problem called a planning game and develop general tools for solving such a game. We then use the tools to investigate a practical buy-and-hold trading problem…

The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines an evolution equation so that in the asymptotic limit a…

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…

We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among…

We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…

A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…

We establish a novel numerical and analytical framework for solving the Korteweg--de Vries (KdV) equation in the negative Sobolev spaces, where classical numerical methods fail due to their reliance on high regularity and inability to…

The paper introduces particle swarm optimization as a viable strategy to find numerical solution of Diophantine equation, for which there exists no general method of finding solutions. The proposed methodology uses a population of integer…

In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the…

Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…

In this work we will develop a new approach to solve the non repayment problem in microfinance due to the problem of asymmetric information. This approach is based on modeling and simulation of ordinary differential systems where time…

Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different…

We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing…