This chapter surveys theoretical research on the long-term performance of fixed-mix investment strategies. These self-financing strategies rebalance the portfolio over time so as to keep constant the proportions of wealth invested in various assets. The main result is that wealth can be grown...

We study front-running by high frequency traders (HFTs) in a limit order model with continuous trading. The model describes an evolutionary equilibrium of low frequency traders (LFTs) who compete in portfolio management services by offering investment styles. The introduction of front-runners...

We explain the evolution of the volatility market and present the infamous day of 'Volmageddon' as an insightful case study. Our survey focuses on the pricing and trading of volatility linked assets, highlighting the impact of mechanical hedging in markets for futures and higher-order...

We explain the evolution of the volatility market and present the infamous day of `Volmageddon' as an insightful case study. Our survey focuses on the pricing and trading of volatility-linked assets, highlighting the impact of mechanical hedging in markets for futures and higher-order...