Browsing by Subject "Sequential switching"

Now showing 1 - 5 of 5

Open Access
An approximate analytical method of analysis of a threshold maintenance policy for a multiphase multicomponent model
(Springer, 2003) Anisimov, V. V.; Gürler, Ü.
A multicomponent system is investigated that consists of n identical unreliable components whose nonfailure operating time consists of a number of sequential phases with exponential times. A maintenance policy is studied that proposes the instant replacement of all the components as soon as the number of components that are in some doubtful state (before a failure) amounts to a predefined threshold value. A cost function averaged over a large period is studied. For a fixed n, an analytical approach is considered. If n increases, a new approximate analytical approach is proposed, which is based on results of the type of the averaging principle for recurrent semi-Markovian processes. The conditions of existence and properties of the optimal strategy are studied. An example is considered and possibilities of generalizations are discussed.
Open Access
Comprehensive lower bounds on sequential prediction
(IEEE, 2014-09) Vanlı, N. Denizcan; Sayın, Muhammed O.; Ergüt, S.; Kozat, Süleyman S.
We study the problem of sequential prediction of real-valued sequences under the squared error loss function. While refraining from any statistical and structural assumptions on the underlying sequence, we introduce a competitive approach to this problem and compare the performance of a sequential algorithm with respect to the large and continuous class of parametric predictors. We define the performance difference between a sequential algorithm and the best parametric predictor as regret, and introduce a guaranteed worst-case lower bounds to this relative performance measure. In particular, we prove that for any sequential algorithm, there always exists a sequence for which this regret is lower bounded by zero. We then extend this result by showing that the prediction problem can be transformed into a parameter estimation problem if the class of parametric predictors satisfy a certain property, and provide a comprehensive lower bound to this case.
Open Access
Growth optimal investment with threshold rebalancing portfolios under transaction costs
(IEEE, 2013) Tunc, S.; Donmez, M.A.; Kozat, Süleyman S.
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.
Open Access
Optimal investment under transaction costs: A threshold rebalanced portfolio approach
(IEEE, 2013) Tunc, S.; Donmez, M. A.; Kozat, S. S.
We study how to invest optimally in a financial market having a finite number of assets from a signal processing perspective. Specifically, we investigate how an investor should distribute capital over these assets and when he/she should reallocate the distribution of the funds over these assets to maximize the expected 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 provided in the paper. As predicted from our derivations, we significantly improve the achieved wealth with respect to the portfolio selection algorithms from the literature on historical data sets under both mild and heavy transaction costs.
Open Access
A unified approach to universal prediction: Generalized upper and lower bounds
(Institute of Electrical and Electronics Engineers Inc., 2015) Vanli, N. D.; Kozat, S. S.
We study sequential prediction of real-valued, arbitrary, and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from computational learning theory, we refrain from any statistical assumptions and define the performance with respect to the class of general parametric predictors. In particular, we present generic lower and upper bounds on this relative performance by transforming the prediction task into a parameter learning problem. We first introduce the lower bounds on this relative performance in the mixture of experts framework, where we show that for any sequential algorithm, there always exists a sequence for which the performance of the sequential algorithm is lower bounded by zero. We then introduce a sequential learning algorithm to predict such arbitrary and unknown sequences, and calculate upper bounds on its total squared prediction error for every bounded sequence. We further show that in some scenarios, we achieve matching lower and upper bounds, demonstrating that our algorithms are optimal in a strong minimax sense such that their performances cannot be improved further. As an interesting result, we also prove that for the worst case scenario, the performance of randomized output algorithms can be achieved by sequential algorithms so that randomized output algorithms do not improve the performance. © 2012 IEEE.