## Pubblicazioni

Pubblicazioni principali più recenti:

### Reaching nirvana with a defaultable asset? (18/05/2017)

*BATTAUZ ANNA, DE DONNO MARZIA AND SBUELZ ALESSANDRO*

Decisions in Economics and Finance (2017) 40:31–52

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)

### The put-call symmetry for American options in the Heston stochastic volatility model (2014)

*BATTAUZ Anna, DE DONNO Marzia and Alessandro SBUELZ*

Mathematical Finance Letters, Vol. 7, 1-8, ISSN 2051-2929 (2014)

- Heston-American-symmetry (137 Kb)

### Kim-Omberg revisited: the duality approach (02/08/2015)

*BATTAUZ Anna, DE DONNO Marzia and Alessandro SBUELZ*

Journal of Probability and Statistics, Vol. 2015, pages 1-6, (2015)

- Kim-Omberg_Revisited-Duality (1.931 Kb)

### Envelope theorems in Banach lattices and asset pricing (19/04/2015)

*BATTAUZ Anna, DE DONNO Marzia and Fulvio ORTU*

Mathematics and Financial Economics , 9:303–323 (2015).

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

### Real options and American derivatives: The double continuation region (12/06/2014)

*BATTAUZ Anna, DE DONNO Marzia, SBUELZ Alessandro*

Management Science, Vol. 61, No. 5, 1094–1107 (2015), http://dx.doi.org/10.1287/mnsc.2013.1891

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)

### Real options and the double continuation region (2012)

*Battauz Anna, Marzia De Donno, Alessandro Sbuelz*

Quantitative Finance, 12, Issue 3, 465- 475, (2012).

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)

### Intertemporal asset pricing and the marginal utility of wealth (2011)

*Battauz Anna, Marzia De Donno, Fulvio Ortu*

Journal of Mathematical Economics, 47, Issue 2, 227-244 (2011).

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)