Marzia De Donno

Real Options and American Derivatives: The Double Continuation Region

We study the nonstandard optimal exercise policy associated with relevant capital investment options and with the prepayment option of widespread collateralized-borrowing contracts like the gold loan. Option exercise is optimally postponed not only when moneyness is insufficient, but also when it is excessive. We extend the classical optimal exercise properties for American options. Early exercise of an American call with a negative underlying payout rate can occur if the option is moderately in the money. We fully characterize the existence, the monotonicity, the continuity, the limits, and the asymptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region. We find that the finite-maturity nonstandard policy conspicuously differs from the infinite-maturity one. This paper was accepted by Jerome Detemple, finance.

Kim and Omberg Revisited: The Duality Approach

We give an alternative duality-based proof to the solution of the expected utility maximization problem analyzed by Kim and Omberg. In so doing, we also provide an example of incomplete-market optimal investment problem for which the duality approach is conducive to an explicit solution.

Envelope theorems in Banach lattices

We derive envelope theorems for optimization problems in which the value function takes values in a general Banach lattice, and not necessarily in the real line. We impose no restriction whatsoever on the choice set. Our result extend therefore the ones of Milgrom and Segal (2002). We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal consumption-portfolio problems in which the utility from consumption is additive but possibly state-dependent and, most importantly, the information structure is not required to be Markovian. In this general setting, the value function is itself a random variable and, if integrable, takes values in a Banach lattice so that our general results can be applied.