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The Third Workshop on
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Trading Mean-reverting Process or Arbitrage under Power
Elena Boguslavskaya, City University, London, Great Britain
Abstract
We solve the position management problem for a power
utility agent trading a mean-reverting asset. This problem arises
in many statistical and fundamental arbitrage trading situations
when the short-term returns on an asset are predictable but
limited risk-bearing capacity does not allow to fully exploit this
predictability. Although the model is quite simple and ignores
some important empiric effects, it reproduces some realistic
patterns of traders' behaviour. We use the Ornstein-Uhlenbeck
process to model the price process and consider a finite horizon
power utility agent. The dynamic programming approach yields a
non-linear PDE. It is solved explicitly, and simple formulas for
the value function and the optimal trading strategy are obtained.
Effects of parameter misspecification are studied using a Monte
Carlo simulation. The talk is based on joint work with
Michael Boguslavsky.