David Shyu

Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. The results in this paper unify, extend, and improve some well-known results in the literature.

Strong and Weak Convergence Theorems for Common Solutions of Generalized Equilibrium Problems and Zeros of Maximal Monotone Operators

The purpose of this paper is to introduce and study two modified hybrid proximal-point algorithms for finding a common element of the solution set EP of a generalized equilibrium problem and the set for two maximal monotone operators and defined on a Banach space . Strong and weak convergence theorems for these two modified hybrid proximal-point algorithms are established.

Relaxed Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of Strictly Pseudocontractive Mappings

We propose a relaxed composite implicit iteration process for finding approximate common fixed points of a finite family of strictly pseudocontractive mappings in Banach spaces. Several convergence results for this process are established.

The Valuation of Information Technology Investments by Real Options Analysis

This study establishes a dynamic model under real options analysis to analyze the optimal timing decision of information technology (IT) investments when the output price for firms is stochastic and benefits of IT investments are arisen from the increasing output price, increasing sale, and cost savings. We derive the closed form expression of the timing of IT investments and furthermore prove that IT investments rise at an increasing rate in economic booms and fall in economic busts. This study finds that increasing (decreasing) price volatility will delay (advance) the timing of IT investments. Increasing IT investments, however, may not delay the timing of IT investments. In addition, the decreasing (increasing) efficiency and increasing (decreasing) depreciation of IT investments will delay (advance) the timing of IT investments.

A model of optimal dynamic asset allocation in a Value-at-Risk framework

This study focuses on the problem of investors in optimising dynamic asset allocation to maximise expected utility under the value-at-risk (VaR) constraint. Although Basak and Shapiro presented this topic, they assumed a complete market and employed the martingale approach to determine a dynamic asset allocation strategy. However, a complete market does not exist in the real world and the martingale approach is not suitable for portfolio selection. Consequently, this study relaxes these limitations and firstly provides a solving method to derive the dynamic asset allocation under the VaR constraint. A simple case and a general case of derivation of optimal dynamic asset allocation are explored. A continuous probability distribution also can be approximated by the discrete probability distribution discussed in this study.