5,108 research outputs found
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 Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation
We propose a numerical recipe for risk evaluation defined by a backward
stochastic differential equation. Using dual representation of the risk
measure, we convert the risk valuation to a stochastic control problem where
the control is a certain Radon-Nikodym derivative process. By exploring the
maximum principle, we show that a piecewise-constant dual control provides a
good approximation on a short interval. A dynamic programming algorithm extends
the approximation to a finite time horizon. Finally, we illustrate the
application of the procedure to financial risk management in conjunction with
nested simulation and on an multidimensional portfolio valuation problem
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
Option pricing with transaction costs using a Markov chain approximation
An efficient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis (in: Dempster, M.A.H., Pliska, S.R. (Eds.), Mathematics of Derivative Securities. Cambridge University Press, Cambridge, UK). A fair option price is determined by requiring that an infinitesimal diversion of funds into the purchase or sale of options has a neutral effect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the option payoff into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely specified option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general definition of an option hedging strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed
Option Pricing with Transaction Costs Using a Markov Chain Approximation
An e cient algorithm is developed to price European options in the pres-
ence of proportional transaction costs, using the optimal portfolio frame-
work of Davis (1997). A fair option price is determined by requiring that
an in nitesimal diversion of funds into the purchase or sale of options
has a neutral e ect on achievable utility. This results in a general option
pricing formula, in which option prices are computed from the solution of
the investor's basic portfolio selection problem, without the need to solve
a more complex optimisation problem involving the insertion of the op-
tion payo into the terminal value function. Option prices are computed
numerically using a Markov chain approximation to the continuous time
singular stochastic optimal control problem, for the case of exponential
utility. Comparisons with approximately replicating strategies are made.
The method results in a uniquely speci ed option price for every initial
holding of stock, and the price lies within bounds which are tight even as
transaction costs become large. A general de nition of an option hedg-
ing strategy for a utility maximising investor is developed. This involves
calculating the perturbation to the optimal portfolio strategy when an
option trade is executed
Evolutionary Stability of Portfolio Rules in Incomplete Markets
This paper studies the evolution of market shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of continuous reinvestment of wealth is determined by the market share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and sufficient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.evolutionary finance; portfolio theory; market selection; incomplete markets
Universal Codes from Switching Strategies
We discuss algorithms for combining sequential prediction strategies, a task
which can be viewed as a natural generalisation of the concept of universal
coding. We describe a graphical language based on Hidden Markov Models for
defining prediction strategies, and we provide both existing and new models as
examples. The models include efficient, parameterless models for switching
between the input strategies over time, including a model for the case where
switches tend to occur in clusters, and finally a new model for the scenario
where the prediction strategies have a known relationship, and where jumps are
typically between strongly related ones. This last model is relevant for coding
time series data where parameter drift is expected. As theoretical ontributions
we introduce an interpolation construction that is useful in the development
and analysis of new algorithms, and we establish a new sophisticated lemma for
analysing the individual sequence regret of parameterised models
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