Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.Comment: Submitted to IEEE Transactions on Signal Processin

Simulation of multi-axis machining processes using z-mapping technique

Parameter selection in machining operations is curial for product quality and high productivity. Process parameters such as feed, spindle speed and depth of cuts are often chosen by trial-error methods. Mathematical models can be employed to predict the mechanics and the dynamics of the process. In this study, Z-mapping technique is utilized to simulate the process step by step by updating the workpiece according the given tool path where the cutter engagement areas are also determined. Using the numerical generalized process model, whole process is simulated for any milling tool geometry including intricate profiling tools, serrated cutters and tools with variable edge geometries