We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be formulated as a composite pure hypothesis testing problem....

Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and...

We study the generalized composite pure and randomized hypothesis testing problems. In addition to characterizing the optimal tests, we examine the conditions under which these two hypothesis testing problems are equivalent, and provide counterexamples when they are not. This analysis is useful...

BitMEX is the largest unregulated bitcoin derivatives exchange, listing contracts suitable for leverage trading and hedging. Using minute-by-minute data, we examine its price discovery and hedging effectiveness. We find that BitMEX derivatives lead prices on major bitcoin spot exchanges. Bid-ask...

The stochastic-alpha-beta-rho (SABR) model has been widely adopted in options trading. In particular, the normal (β=0) SABR model is a popular model choice for interest rates because it allows negative asset values. The option price and delta under the SABR model are typically obtained via...

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive Bessel function evaluations. We propose a new exact simulation scheme without the Bessel function, based on the observation that the conditional...