680 research outputs found
On using shadow prices in portfolio optimization with transaction costs
In frictionless markets, utility maximization problems are typically solved
either by stochastic control or by martingale methods. Beginning with the
seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713],
stochastic control theory has also been used to solve various problems of this
type in the presence of proportional transaction costs. Martingale methods, on
the other hand, have so far only been used to derive general structural
results. These apply the duality theory for frictionless markets typically to a
fictitious shadow price process lying within the bid-ask bounds of the real
price process. In this paper, we show that this dual approach can actually be
used for both deriving a candidate solution and verification in Merton's
problem with logarithmic utility and proportional transaction costs. In
particular, we determine the shadow price process.Comment: Published in at http://dx.doi.org/10.1214/09-AAP648 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions
Currently, most of the basic mechanisms governing tumor-immune system
interactions, in combination with modulations of tumor-associated vasculature,
are far from being completely understood. Here, we propose a mathematical model
of vascularized tumor growth, where the main novelty is the modeling of the
interplay between functional tumor vasculature and effector cell recruitment
dynamics. Parameters are calibrated on the basis of different in vivo
immunocompromised Rag1-/- and wild-type (WT) BALB/c murine tumor growth
experiments. The model analysis supports that tumor vasculature normalization
can be a plausible and effective strategy to treat cancer when combined with
appropriate immuno-stimulations. We find that improved levels of functional
tumor vasculature, potentially mediated by normalization or stress alleviation
strategies, can provide beneficial outcomes in terms of tumor burden reduction
and growth control. Normalization of tumor blood vessels opens a therapeutic
window of opportunity to augment the antitumor immune responses, as well as to
reduce the intratumoral immunosuppression and induced-hypoxia due to vascular
abnormalities. The potential success of normalizing tumor-associated
vasculature closely depends on the effector cell recruitment dynamics and tumor
sizes. Furthermore, an arbitrary increase of initial effector cell
concentration does not necessarily imply a better tumor control. We evidence
the existence of an optimal concentration range of effector cells for tumor
shrinkage. Based on these findings, we suggest a theory-driven therapeutic
proposal that optimally combines immuno- and vaso-modulatory interventions
The dual optimizer for the growth-optimal portfolio under transaction costs
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar et al.(Math. Oper. Res. 13:277-294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341-1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rat
Equilibrium asset pricing with transaction costs
We study risk-sharing economies where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully coupled forward–backward stochastic differential equations. We show that a unique solution exists provided that the agents’ preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the empirically observed illiquidity discounts and liquidity premia correspond to a positive relationship between transaction costs and volatility
Goal-seeking compresses neural codes for space in the human hippocampus and orbitofrontal cortex
Humans can navigate flexibly to meet their goals. Here, we asked how the neural representation of allocentric space is distorted by goal-directed behavior. Participants navigated an agent to two successive goal locations in a grid world environment comprising four interlinked rooms, with a contextual cue indicating the conditional dependence of one goal location on another. Examining the neural geometry by which room and context were encoded in fMRI signals, we found that map-like representations of the environment emerged in both hippocampus and neocortex. Cognitive maps in hippocampus and orbitofrontal cortices were compressed so that locations cued as goals were coded together in neural state space, and these distortions predicted successful learning. This effect was captured by a computational model in which current and prospective locations are jointly encoded in a place code, providing a theory of how goals warp the neural representation of space in macroscopic neural signals
Goal-seeking compresses neural codes for space in the human hippocampus and orbitofrontal cortex
Humans can navigate flexibly to meet their goals. Here, we asked how the neural representation of allocentric space is distorted by goal-directed behavior. Participants navigated an agent to two successive goal locations in a grid world environment comprising four interlinked rooms, with a contextual cue indicating the conditional dependence of one goal location on another. Examining the neural geometry by which room and context were encoded in fMRI signals, we found that map-like representations of the environment emerged in both hippocampus and neocortex. Cognitive maps in hippocampus and orbitofrontal cortices were compressed so that locations cued as goals were coded together in neural state space, and these distortions predicted successful learning. This effect was captured by a computational model in which current and prospective locations are jointly encoded in a place code, providing a theory of how goals warp the neural representation of space in macroscopic neural signals.</p
- …