10,686 research outputs found
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
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
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Optimal portfolio control with trading strategies of finite variation
We propose a method for portfolio selection where the trading strategies are constrained to have a finite variation. A simulation example shows a significant reduction in trasaction costs as compared to log-optimal portfolio, for almost same final wealth
Growth-optimal portfolios under transaction costs
This paper studies a portfolio optimization problem in a discrete-time
Markovian model of a financial market, in which asset price dynamics depend on
an external process of economic factors. There are transaction costs with a
structure that covers, in particular, the case of fixed plus proportional
costs. We prove that there exists a self-financing trading strategy maximizing
the average growth rate of the portfolio wealth. We show that this strategy has
a Markovian form. Our result is obtained by large deviations estimates on
empirical measures of the price process and by a generalization of the
vanishing discount method to discontinuous transition operators.Comment: 32 page
Efficient option pricing with transaction costs
A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed
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Migration, credit markets, moral hazard, interlinkage.
A fast numerical algorithm is developed to price European options with
proportional transaction costs using the utility maximization framework
of Davis (1997). This approach allows option prices to be computed by
solving the investor's basic portfolio selection problem, without the inser-
tion of the option payo into the terminal value function. The properties
of the value function can then be used to drastically reduce the number of
operations needed to locate the boundaries of the no transaction region,
which leads to very e cient option valuation. The optimization problem
is solved numerically for the case of exponential utility, and comparisons
with approximately replicating strategies reveal tight bounds for option
prices even as transaction costs become large. The computational tech-
nique involves a discrete time Markov chain approximation to a continuous
time singular stochastic optimal control problem. A general de nition of
an option hedging strategy in this framework is developed. This involves
calculating the perturbation to the optimal portfolio strategy when an
option trade is execute
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