Halil Mete Soner

Martingale Optimal Transport in the Skorokhod Space

The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints are required to hold for every path in the Skorokhod space. This problem has the financial interpretation as the robust hedging of path dependent European options.

Liquidity Models in Continuous and Discrete Time

We survey several models of liquidity and liquidity-related problems such as optimal execution of a large order, hedging and super-hedging options for a large trader, utility maximization in illiquid markets, and price impact models with price manipulation strategies.