14 research outputs found
Multi-Period Trading via Convex Optimization
We consider a basic model of multi-period trading, which can be used to
evaluate the performance of a trading strategy. We describe a framework for
single-period optimization, where the trades in each period are found by
solving a convex optimization problem that trades off expected return, risk,
transaction cost and holding cost such as the borrowing cost for shorting
assets. We then describe a multi-period version of the trading method, where
optimization is used to plan a sequence of trades, with only the first one
executed, using estimates of future quantities that are unknown when the trades
are chosen. The single-period method traces back to Markowitz; the multi-period
methods trace back to model predictive control. Our contribution is to describe
the single-period and multi-period methods in one simple framework, giving a
clear description of the development and the approximations made. In this paper
we do not address a critical component in a trading algorithm, the predictions
or forecasts of future quantities. The methods we describe in this paper can be
thought of as good ways to exploit predictions, no matter how they are made. We
have also developed a companion open-source software library that implements
many of the ideas and methods described in the paper
AN EFFICIENT METHOD FOR COMPRESSED SENSING
Compressed sensing or compressive sampling (CS) has been receiving a lot of interest as a promising method for signal recovery and sampling. CS problems can be cast as convex problems, and then solved by several standard methods such as interior-point methods, at least for small and medium size problems. In this paper we describe a specialized interiorpoint method for solving CS problems that uses a preconditioned conjugate gradient method to compute the search step. The method can efficiently solve large CS problems, by exploiting fast algorithms for the signal transforms used. The method is demonstrated with a medical resonance imaging (MRI) example. Index Terms — compressed sensing, compressive sampling, ℓ1 regularization, interior-point methods, preconditioned conjugate gradients. 1.1. Compressed sensing 1