Time-varying asset returns lead highly risk-averse investors to choose market-timing exposures that increase in their horizon, in agreement with the common advice to reduce risk with age, but in contrast to theoretical work that prescribes constant portfolio weights. In a market where an...

In the high-frequency limit, conditional expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon, and making dynamic optimization problems tractable. We find an explicit formula for locally...

In portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real...

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...