We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost...

We study a stochastic control approach to managed futures portfolios. Building on the Schwartz (1997) stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity futures or multiple futures contracts over a finite...

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit...

An optimization approach is proposed to construct sparse portfolios with mean-reverting price behaviors. Our objectives are threefold: (i) design a multi-asset long-short portfolio that best fits an Ornstein-Uhlenbeck process in terms of maximum likelihood, (ii) select portfolios with desirable...

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a...

In this paper, we analyze the process of constructing cointegrated portfolios of cryptocurrencies. Our procedure involves a series of statistical tests, including the Johansen cointegration test and Engle-Granger two-step approach. Among our results, we construct cointegrated portfolios...

We study a mean-field game framework in which agents expend costly efforts in order to transition into a state where they receive cash flows. As more agents transition into the cash flow receiving state, the magnitude of all remaining cash flows decreases, introducing an element of competition...

We study the problem of dynamically trading a pair of futures contracts. We consider a two-factor mean-reverting model, where the spot price tends to evolve around its stochastic equilibrium that is also mean-reverting. We derive the futures price dynamics and determine the optimal futures...

We study an optimization-based approach to construct a mean-reverting portfolio of assets. Our objectives are threefold: (1) design a portfolio that is well-represented by an Ornstein-Uhlenbeck process with parameters estimated by maximum likelihood, (2) select portfolios with desirable...

We study the problem of hedging early exercise (American) options with respect to exponential utility within a general incomplete market model. This leads us to construct a duality formula involving relative entropy minimization and optimal stopping. We further consider claims with multiple...