Growth optimal investment in discrete-time markets with proportional transaction costs
| Autor: | N. Denizcan Vanli, Suleyman S. Kozat, Sait Tunc, Mehmet A. Donmez |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Signal processing
Mathematical optimization Discrete-time stock market Portfolio selection problems Computer science Discrete time 02 engineering and technology Proportional transaction costs Optimal portfolio selection Artificial Intelligence 0202 electrical engineering electronic engineering information engineering Investments Electrical and Electronic Engineering Continuous distribution Brownian motion Growth optimal portfolio Transaction cost Sequence Stationary distribution Markov chain Rebalancing Financial markets Markov processes Applied Mathematics Commerce Chains Sampling (statistics) Continuous time systems 020206 networking & telecommunications Maximum likelihood estimation Threshold rebalancing Proportional transaction cost Costs Computational Theory and Mathematics Discrete time and continuous time Optimal portfolios Maximum likelihood estimator Signal Processing Portfolio 020201 artificial intelligence & image processing Sequential switching Computer Vision and Pattern Recognition Statistics Probability and Uncertainty Maximum likelihood |
| Zdroj: | Digital Signal Processing: A Review Journal |
| Popis: | Achieving optimal expected growth in i.i.d. discrete-time markets.Efficient recursive calculation via an irreducible Markov chain formulation.Successful application to Brownian markets and historical data. 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. |
| Databáze: | OpenAIRE |
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