A novel method to analyze the impact of transaction costs on a dynamically optimized portfolio is developed. Transaction costs, when taken into account in an incomplete market, generate a liquidity premium which is large enough to address important economic questions, such as the size of the...

We investigate the optimal investment problem when the interest rate is stochastic and the investor must pay proportional transaction costs when buying and selling the risky assets. We first consider a portfolio of bonds and transaction costs.We then add a stock to the portfolio, and analyze the...

We construct a simple measure to quantify the level of market efficiency. We apply this measure to investigate the level of market efficiency and analyze its variation over time. The main contribution of the new measure is that it makes it easy to compare market efficiency across assets, time,...

We show that the level of market-efficiency in the five largest cryptocurrencies is highly time-varying. Specifically, before 2017, cryptocurrency-markets are mostly inefficient. This corroborates recent results on the matter. However, the cryptocurrency-markets become more efficient over time...