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

A Deterministic Analysis of an Online Convex Mixture of Expert Algorithms

Cataloged from PDF version of article.We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to model an unknown desired signal. This online learning algorithm is shown to achieve (and in some cases outperform) the mean-square error (MSE) performance of the best constituent algorithm in the mixture in the steady-state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals and systems. Hence, such an analysis may not be useful or valid for signals generated by various real life systems that show high degrees of nonstationarity, limit cycles and, in many cases, that are even chaotic. In this paper, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the time-accumulated squared estimation error of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples. © 2012 IEEE

On the oscillatory behavior of even order neutral delay dynamic equations on time-scales

We establish some new criteria for the oscillation of the even order neutral dynamic equation \begin{equation*} \left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha }\right) ^{\Delta }+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda }=0 \end{equation*} on a time scale $\mathbb{T}$, where $n \geq 2$ is even, $\alpha$ and $\lambda$ are ratios of odd positive integers, $a$, $p$ and $q$ are real valued positive rd-continuous functions defined on $\mathbb{T}$, and $g$ and $\tau$ are real valued rd-continuous functions on $\mathbb{T}$. Examples illustrating the results are included

X-ray induced reduction of Au and Pt ions on silicon substrates

Prolonged exposure to X-rays of HAuCl4, PtCl4 and their mixtures, deposited from an aqueous solution onto a silicon substrate, causes chemical reduction of the metal ions to their metallic states. The corresponding oxidation reaction is the conversion of chloride ions to chlorine. The resultant metal atoms aggregate to form metallic/bimetallic nanoclusters as evidenced from their XPS chemical shifts. Hence, X-rays are usable for in-situ nanoparticle production or for direct-writing applications on silicon substrates. © 2007 Elsevier B.V. All rights reserved

Growth optimal investment with threshold rebalancing portfolios under transaction costs

We study how to invest optimally in a stock market having a finite number of assets from a signal processing perspective. 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. This is achieved by 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. © 2013 IEEE

Preparation of Au and Au-Pt nanoparticles within PMMA matrix using UV and X-ray irradiation

Au and Au-Pt alloy nanoparticles are prepared and patterned at room temperature within the PMMA polymer matrix by the action of 254 nm UV light or X-rays. The polymer matrix enables us to entangle the kinetics of the photochemical reduction from the nucleation and growth processes, when monitored by UV-vis spectroscopy. Accordingly, increase of the temperature to 50 °C of the reaction medium increases the nucleation and growth rates of the nanoparticle formation by more than one order of magnitude, due to enhanced diffusion and nucleation at the higher temperature, but has no effect on the photochemical reduction process. Presence of Pt ions also increases the same rate, but by a factor two only. Similar photochemical reduction and particle growth take also place within the PMMA matrix, when these metal ions are subjected to prolonged exposure to X-rays, as evidenced by XPS analysis. Both angle-resolved and charge-contrast measurements using XPS reveal that the resultant Au and Pt species are in close proximity to each other, indicating the Au-Pt alloy formation to be the most likely case. © 2008 Elsevier Ltd. All rights reserved

Growth optimal investment in discrete-time markets with proportional transaction costs

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we also solve the optimal portfolio selection problem in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations