We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions...

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...

This paper considers a multi-agent optimal investment problem with conservative sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative sentiments of the agents by a sup-inf/inf-sup problem where we take infimum on a choice of a probability measure and...