We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $\epsilon$ small, which leads to the optimization problem having an...

This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset's drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the...

This article explores the relationship between option markets for the S&P500 (SPX) and CBOE's Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides...

We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and...

We consider the problem of filtering and control in the setting of portfolio optimization in financial markets with random factors that are not directly observable. The example that we present is a commodities portfolio where yields on futures contracts are observed with some noise. Through the...

This paper considers the problem of portfolio optimization in a market with partial information and discretely observed price processes. Partial information refers to the setting where assets have unobserved factors in the rate of return and the level of volatility. Standard filtering techniques...