We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

Using techniques from deep learning, we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by Föllmer and Leukert. Not only does this approach better accommodate the realistic setting of...

Using techniques from deep learning, we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by Föllmer and Leukert. Not only does this approach better accommodate the realistic setting of...

In this article we survey methods of dealing with the following problem: A financial agent is trying to hedge a claim C, without having enough initial capital to perform a perfect (super) replication. In particular, we describe results for minimizing the expected loss of hedging the claim C both...

We investigate the partial hedging problem in financial markets with a large agent. An agent is said to be large if his/her trades influence the equilibrium price. We develop a stochastic differential equation (SDE) with a single large agent parameter to model such a market. We focus on...

We propose a model in which mergers exert a more pronounced effect on the structure of a market than simply reducing the number of competitors. We show that this may render horizontal mergers profitable and welfare-improving even if costs are linear. The results help to reconcile theory with...