Reaching nirvana with a defaultable asset?

摘要

We study the optimal dynamic portfolio exposure to predictable default risk, taking inspiration from the search for yield by means of defaultable assets observed before the 2007-2008 crisis and in its aftermath. Under no arbitrage, default risk is compensated by an 'yield pickup' that can strongly attract aggressive investors via an investment-horizon effect in their optimal non-myopic portfolios. We show it by stating the optimal dynamic portfolio problem of Kim and Omberg (Rev Financ Stud 9:141-161, 1996) for a defaultable risky asset and by rigorously proving the existence of nirvana-type solutions. We achieve such a contribution to the portfolio optimization literature by means of a careful, closed-form-yielding adaptation to our defaultable asset setting of the general convex duality approach of Kramkov and Schachermayer (Ann Appl Probab 9(3):904-950, 1999; Ann Appl Probab 13(4):1504-1516, 2003).