Candidate: Adam Daniel Gomes
Title: Hedging in a Financial Market with Regime-Switching
Date: January 27, 2021
Time: 12:30 PM
Place: REMOTE ATTENDANCE
Supervisor(s): Heunis, Andrew
Abstract:
We address a problem of hedging within a regime-switching market model with both convex portfolio constraints and general margin requirements. It is well-known that in a complete financial market model driven by Brownian motion, one can always perfectly hedge a given contingent claim B starting from an appropriate initial wealth x. However, when portfolio constraints are imposed on a Brownian motion market model, the financial market is rendered incomplete and one can generally only promise to super-hedge the claim B (see El-Karoui and Quenez (1995) and Cvitanic and Karatzas (1993)). That is, one can only construct a portfolio which almost-surely exceeds, rather than replicates, the contingent claim B at close of trade. In regime-switching market models, the market parameters are adapted not only to the filtration of a given Brownian motion, but to the joint filtration of a Brownian motion together with a regime-switching Markov chain, causing the market to be incomplete. We therefore use the approach of Cvitanic and Karatzas (1993) to characterize a super-hedging strategy for the contingent claim B in a constrained regime-switching market model and determine that the least initial wealth is given by a supremum taken over an appropriate space of dual variables. Complementary to these results is another, which asserts that if the supremum which defines the appropriate initial wealth is actually attained, then one can indeed perfectly hedge the contingent claim B in a constrained Brownian motion market model. We propose to establish an analog of this latter result in a constrained market model in which incompleteness arises from both portfolio constraints and regime-switching.