11,236 research outputs found
Utility maximization in incomplete markets
We consider the problem of utility maximization for small traders on
incomplete financial markets. As opposed to most of the papers dealing with
this subject, the investors' trading strategies we allow underly constraints
described by closed, but not necessarily convex, sets. The final wealths
obtained by trading under these constraints are identified as stochastic
processes which usually are supermartingales, and even martingales for
particular strategies. These strategies are seen to be optimal, and the
corresponding value functions determined simply by the initial values of the
supermartingales. We separately treat the cases of exponential, power and
logarithmic utility.Comment: Published at http://dx.doi.org/10.1214/105051605000000188 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment
We introduce a linear space of finitely additive measures to treat the
problem of optimal expected utility from consumption under a stochastic clock
and an unbounded random endowment process. In this way we establish existence
and uniqueness for a large class of utility-maximization problems including the
classical ones of terminal wealth or consumption, as well as the problems that
depend on a random time horizon or multiple consumption instances. As an
example we explicitly treat the problem of maximizing the logarithmic utility
of a consumption stream, where the local time of an Ornstein-Uhlenbeck process
acts as a stochastic clock.Comment: Published at http://dx.doi.org/10.1214/105051604000000738 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Optimal investment with intermediate consumption under no unbounded profit with bounded risk
We consider the problem of optimal investment with intermediate consumption
in a general semimartingale model of an incomplete market, with preferences
being represented by a utility stochastic field. We show that the key
conclusions of the utility maximization theory hold under the assumptions of no
unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal
and dual value functions.Comment: 10 pages, revised version, to appear in the Applied Probability
Journal
Processing second-order stochastic dominance models using cutting-plane representations
This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian
National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)
Stability of exponential utility maximization with respect to market perturbations
We investigate the continuity of expected exponential utility maximization
with respect to perturbation of the Sharpe ratio of markets. By focusing only
on continuity, we impose weaker regularity conditions than those found in the
literature. Specifically, we require, in addition to the -compactness
hypothesis of Larsen and \v{Z}itkovi\'c (2007) (ArXiv: 0706.0474), a local
hypothesis, a condition which is seen to always be trivially satisfied in
the setting of Larsen and \v{Z}itkovi\'c (2007). For markets of the form , these conditions are simultaneously implied by the
existence of a uniform bound on the norm of in a suitable
space.Comment: Final version. To appear in "Stochastic Processes and Their
Applications
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