We solve for the first time a longstanding puzzle of quantitative finance that has often been
described as the holy grail of volatility modelling: build a model that jointly and exactly …

Abstract We introduce a Benamou–Brenier formulation for the continuous-time martingale
optimal transport problem as a weak length relaxation of its discrete-time counterpart. By the …

In this paper, we introduce and develop the theory of semimartingale optimal transport in a
path dependent setting. Instead of the classical constraints on marginal distributions, we …

This paper addresses the problem of utility maximization under uncertain parameters. In
contrast with the classical approach, where the parameters of the model evolve freely within …

We show how inter-asset dependence information derived from market prices of options can
lead to improved model-free price bounds for multi-asset derivatives. Depending on the type …

Predicting volatility is important for asset predicting, option pricing and hedging strategies
because it cannot be directly observed in the financial market. The dynamics of the volatility …

The Bass Local Volatility Model (Bass-LV), as studied in\citep {henry2021bass}, stands out
for its ability to eliminate the need for interpolation between maturities. This offers a …

By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we
derive consequences for fully nonlinear parabolic equations of the form $\dt v+ F (t, x, D …

The present work is devoted to investigating portfolio optimization from different
perspectives. We consider continuous-time investment on a finite time horizon. In the first …