Hedging costs for two large investors

Abstract

We consider the cost of hedging contingent claims in a financial market where the trades of two large investors can move market prices. We provide a characterization of the minimal hedging costs in terms of associated stochastic control problems. We also prove that the minimal hedging cost is a viscosity solution of a corresponding dynamic programming equation in the case of a Markov market model.

Keywords:

• large investor
• hedging cost
• dynamic programming equation

AMS Subject Classification::

• 49J20
• 49L25
• 91B28
• 93E20

Notes

1. For a standard asset pricing theory, see the usual textbooks, e.g. Duffie [10], Karatzas [14] and Karatzas and Shreve [15].

2. See Lemma 3.5.3 in Karatzas and Screve [17] and Exercise 0.3.6 in Karatzas [14].