Duality Theory for Portfolio Optimisation under Transaction Costs

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a predictable and an optional strong supermartingale and pertains to all strategies which remain solvent under transaction costs. We provide examples showing that in the present general setting the shadow price process has to be of this generalised form

Strong supermartingales and limits of nonnegative martingales

Given a sequence $(M^n)^{\infty}_{n=1}$ of nonnegative martingales starting at $M^n_0=1$, we find a sequence of convex combinations $(\widetilde{M}^n)^{\infty}_{n=1}$ and a limiting process $X$ such that $(\widetilde{M}^n_{\tau})^{\infty}_{n=1}$ converges in probability to $X_{\tau}$, for all finite stopping times $\tau$. The limiting process $X$ then is an optional strong supermartingale. A counterexample reveals that the convergence in probability cannot be replaced by almost sure convergence in this statement. We also give similar convergence results for sequences of optional strong supermartingales $(X^n)^{\infty}_{n=1}$, their left limits $(X^n_-)^{\infty}_{n=1}$ and their stochastic integrals $(\int\varphi \,dX^n)^{\infty}_{n=1}$ and explain the relation to the notion of the Fatou limit.Comment: Published at http://dx.doi.org/10.1214/14-AOP970 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility maximisation under transaction costs by establishing the existence of a so-called shadow price. This is a semimartingale price process, taking values in the bid ask spread, such that frictionless trading for that price process leads to the same optimal strategy and utility as the original problem under transaction costs. Our results combine arguments from convex duality with the stickiness condition introduced by P. Guasoni. They apply in particular to exponential utility and geometric fractional Brownian motion. In this case, the shadow price is an Ito process. As a consequence we obtain a rather surprising result on the pathwise behaviour of fractional Brownian motion: the trajectories may touch an Ito process in a one-sided manner without reflection.Comment: To appear in Annals of Applied Probability. We would like to thank Junjian Yang for careful reading of the manuscript and pointing out a mistake in an earlier versio

Fermi Surface of the 2D Hubbard Model at Weak Coupling

We calculate the interaction-induced deformation of the Fermi surface in the two-dimensional Hubbard model within second order perturbation theory. Close to half-filling, interactions enhance anisotropies of the Fermi surface, but they never modify the topology of the Fermi surface in the weak coupling regime.Comment: 4 pages, LaTeX2e, 5 embedded EPS figures, accepted to be published in Z. Phys.

OLS-based estimation of the disturbance variance under spatial autocorrelation

We investigate the OLS-based estimator s2 of the disturbance variance in the standard linear regression model with cross section data when the disturbances are homoskedastic, but spatially correlated. For the most popular model of spatially autoregressive disturbances, we show that s2 can be severely biased in finite samples, but is asymptotically unbiased and consistent for most types of spatial weighting matrices as sample size increases. --regression,spatial error correlation,bias,variance

Landau-Vlasov model versus Vlasov-Uehling-Uhlenbeck-approach : different flow effects from the same theory?

Differences between the Nantes-Ganil-Grenoble (NGG) LV-model and the original VUU approach are analysed. It is found that the LV code tends to simulate - for small timesteps - a non-viscous testparticle fluid

Role of cytochrome c heme lyase in the import of cytochrome c into mitochondria

The import of cytochrome c into Neurospora crassa mitochondria was examined at distinct stages in vitro. The precursor protein, apocytochrome c, binds to mitochondria with high affinity and specificity but is not transported completely across the outer membrane in the absence of conversion to holocytochrome c. The bound apocytochrome c is accessible to externally added proteases but at the same time penetrates far enough through the outer membrane to interact with cytochrome c heme lyase. Formation of a complex in which apocytochrome c and cytochrome c heme lyase participate represents the rate-limiting step of cytochrome c import. Conversion from the bound state to holocytochrome c, on the other hand, occurs 10-30-fold faster. Association of apocytochrome c with cytochrome c heme lyase also takes place after solubilizing mitochondria with detergent. We conclude that the bound apocytochrome c, spanning the outer membrane, forms a complex with cytochrome c heme lyase from which it can react further to be converted to holocytochrome c and be translocated completely into the intermembrane space

Incommensurate nematic fluctuations in the two-dimensional Hubbard model

We analyze effective d-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive d-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the d-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.Comment: 8 pages, 4 figures; figures improve

Transition from binary processes to multifragmentation in quantum molecular dynamics for intermediate-energy heavy ion collisions

We study the transition from fusion-fission phenomena at about 20 MeV/nucleon multifragmentation at 100–200 MeV/nucleon in the reaction 16O+80Br employing the quantum molecular dynamics model. The time evolution of the density and mass distribution, the charged-particle multiplicity, and spectra as well as angular distributions of light particles are investigated. The results exhibit the transition of the disassembly mechanism, but no sharp change is found. The results are in good agreement with recently measured 4-Pi data