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PublicationsRecent main publications: 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 20072008 crisis and in its aftermath. Under no arbitrage, default risk is compensated by an `yield pickup' that can strongly attract aggressive investors via an investmenthorizon effect in their optimal nonmyopic portfolios. We show it by extending the optimal dynamic nirvanatype portfolio problem of Kim and Omberg (1996) to a defaultable risky asset and by rigorously proving their longstanding nirvanasolution conjecture. We achieve such a contribution to the portfolio optimization literature by means of a careful, closed formyielding adaptation to our defaultableasset setting of the general convex duality approach of Kramkov and Schachermayer (1999, 2003). Last change 04/12/2019 The putcall symmetry for American options in the Heston stochastic volatility model (2014) BATTAUZ Anna, DE DONNO Marzia and Alessandro SBUELZ Mathematical Finance Letters, Vol. 7, 18, ISSN 20512929 (2014) For the American putcall 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. Last change 19/07/2016 KimOmberg revisited: the duality approach (02/08/2015) BATTAUZ Anna, DE DONNO Marzia and Alessandro SBUELZ Journal of Probability and Statistics, Vol. 2015, pages 16, (2015)
We give an alternative dualitybased proof to the solution of the expected utility maximization problem analyzed by Kim and Omberg. In so doing,we also provide an example of incompletemarket optimal investment problem forwhich the duality approach is conducive to an explicit solution. Last change 16/05/2016 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). 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 welldefined notion of marginal utility of wealth in optimal discretetime, finitehorizon consumptionportfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency. Last change 16/05/2016 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 nonstandard optimal exercise policy associated with relevant capital investment options and with the prepayment option of widespread collateralizedborrowing 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 finitematurity nonstandard policy conspicuously differs from the infinitematurity one. Last change 16/05/2016 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 riskadjusted growth rate of the project’s present value V overcomes the discount rate but is dominated by the average riskadjusted growth rate of the cost I of entering the project, a nonstandard 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
Last change 25/11/2013 Intertemporal asset pricing and the marginal utility of wealth (2011) Battauz Anna, Marzia De Donno, Fulvio Ortu Journal of Mathematical Economics, 47, Issue 2, 227244 (2011). We consider the general class of discretetime, finitehorizon intertemporal asset pricing models in which preferences for consumption at the intermediate dates are allowed to be statedependent, satiated, nonconvex 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 stateprice 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/riskneutral probabilities commonly employed in derivative asset pricing theory. We supply an example in which our characterization holds while the standard representation of stateprice densities in terms of marginal utilities of optimal consumption fails.
Keywords: arbitrage, viability, linear pricing rules, optimal portfolioconsumption problems, marginal utility of wealth. Last change 25/11/2013 Last updated November 30, 2011
