ANNA BATTAUZ

We study the optimal dynamic portfolio exposure to predictable default risk to explain 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 extending the optimal dynamic nirvana-type portfolio problem of Kim and Omberg (1996) to a defaultable risky asset and by rigorously proving their longstanding nirvana-solution conjecture. 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 (1999, 2003).

• Battauz-DeDonno-Sbuelz_Nirvana (834 Kb)

For the American put-call option symmetry in the Heston (1993) model, we provide a new and simple proof that is easily  accessible to the general finance readership. We also characterize the link between the freeboundary of the American call and the free boundary of the symmetric American put.

• Heston-American-symmetry (137 Kb)

• Kim-Omberg_Revisited-Duality (1.931 Kb)

We develop envelope theorems for optimization problems in which the value function takes values in a general Banach lattice. We consider both the special case of a convex choice set and a concave objective function and the more general case case of an arbitrary choice set and a general objective function. We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal discrete-time, finite-horizon consumption-portfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency.

• Envelope-theorems-in-Banach-lattices (377 Kb)

We study the non-standard 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 non-standard policy conspicuously differs from the infinite-maturity one.

• Workshop_Optimal_stopping_applications_TO2015_slides_battauz (411 Kb)
• Bocconi Knowledge, July 2nd, 2014: Gold Loans (85 Kb - english version)
• Bocconi Knowledge, 2 luglio 2014: i gold loans. (82 Kb - italian version)
• battauz-dedonno-sbulez-forthcoming-management-science (326 Kb)

If the average risk-adjusted growth rate of the project’s present value V overcomes the discount rate but is dominated by the average risk-adjusted growth rate of the cost I of entering the project, a non-standard double continuation region can arise: The firm waits to invest in the project if V is insufficiently above I as well as if V is comfortably above I. Under a framework with diffusive uncertainty, we give exact characterization to the value of the option to invest, to the structure of the double continuation region, and to the subset of the

primitives’ values that support such a region.

Keywords: Asset pricing; American options; Capital investment theory; Optimal stopping;

Free boundary

• real-options-double-continuation (160 Kb)

We consider the general class of discrete-time, finite-horizon intertemporal asset pricing models in which preferences for consumption at the intermediate dates are allowed to be state-dependent, satiated, non-convex and discontinuous, and the information structure is not required to be generated by a Markov process of state variables. We supply a generalized de.nition of marginal utility of wealth based on the Fréchet differential of

the value operator that maps time t wealth into maximum conditional remaining utility.  We show that in this general case all state-price densities/stochastic discount factors are fully characterized by the marginal utility of wealth of optimizing agents even if their preferences for intermediate consumption are highly irregular. Our result requires only the strict monotonicity of preferences for terminal wealth and the existence of a portfolio with positive and bounded gross returns. We also relate our generalized notion of marginal utility of wealth to the equivalent martingale measures/risk-neutral probabilities commonly employed in derivative asset pricing theory. We supply an example in which our characterization holds while the standard representation of state-price densities in terms of marginal utilities of optimal consumption fails.

Keywords: arbitrage, viability, linear pricing rules, optimal portfolio-consumption problems, marginal utility of wealth.

• marginal-utility-wealth (341 Kb)