In a market with price-impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long-term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities...

This paper finds optimal portfolios for the reference-dependent preferences of Koszegi and Rabin, with piecewise linear gain-loss utility, in a one-period model with a safe and a risky asset. If the return of the risky asset is highly dispersed relative to its potential gains, two personal...

We find equilibrium stock prices and interest rates in a representative-agent model where dividend growth is uncertain, but gradually revealed by dividends themselves, while asset prices reflect current information and the potential impact of future knowledge. In addition to the usual premium...

Leveraged and inverse exchange-traded funds seek daily returns equal to fixed multiples of indexes' returns. Trading costs implied by frequent adjustments of funds' portfolios create a tension between tracking error, reflecting short-term correlation with the index, and excess return, the...

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity...

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We...

For any positive diffusion with minimal regularity, there exists a semimartingale, with uniformly close paths, which is a martingale under an equivalent probability. As a result, in models of asset prices based on such diffusions, arbitrage and bubbles alike disappear under proportional...

A growing literature suggests that even in the absence of any ability to predict returns, holding options on the benchmarks or trading frequently can generate positive alpha. The ratio of alpha to its tracking error appraises a fund's performance. This paper derives the performance-maximizing...

Recent progress in portfolio choice has made a wide class of problems involving transaction costs tractable. We review the basic approach to these problems, and outline some directions for future research