Optimal Dynamic rading Strategies with Risk Limits

Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios.Yet,existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular,VaR limits have been found to induce increased risk exposure in some states and an increased probability of extreme losses. However, these conclusions are based on models that are either static or dynamically inconsistent. In this paper we formulate a dynamically consistent model of optimal portfolio choice subject to VaR limits and show that the conclusions of earlier papers are incorrect if, consistently with common practice,the portfolio VaR is reevaluated dynamically making use of available conditioning information. In particular, we ?nd that the risk exposure of a trader subject to a VaR limit is always lower than that of an unconstrained trader and that the probability of extreme losses is also lower.We also consider risk limits formulated in terms of Tail Conditional Expectation (TCE),a coherent risk measure often advocated as an alternative to VaR,and show that in our dynamic setting it is always possible to transform a TCE limit into an equivalent VaR limit,and conversely.

A twist in chiral interaction between biological helices

Using an exact solution for the pair interaction potential, we show that long, rigid, chiral molecules with helical surface charge patterns have a preferential interaxial angle ~((RH)^1/2)/L, where L is the length of the molecules, R is the closest distance between their axes, and H is the helical pitch. Estimates based on this formula suggest a solution for the puzzle of small interaxial angles in a-helix bundles and in cholesteric phases of DNA.Comment: 7 pages, 2 figures, PDF file onl

van der Waals Interactions in Cholesteric Liquid Crystals

Microscopic calculations of the pitch of cholesteric liquid crystals are based on a few types of interactions between molecules: (1) short-range repulsive, (2) direct Coulomb, and (3) long-range van der Waals interactions. Recently, it was shown that first two types cannot be treated in the frame of mean-field approximation. Here we show that, contrary to common belief, an accurate evaluation of the intermolecular dispersion forces contributing to chiral ordering requires consideration of biaxial correlations between molecules which are neglected in the mean-field approximation. We found that in the presence of biaxial correlations chiral interactions depend very weakly on the anisotropy of the local (i.e., atomic) polarizability. Instead, the chiral interaction between two molecules is dominated by the character of biaxial correlations, the isotropic part of local polarizability of one molecule, and a chiral parameter of the other molecule, which characterizes the chiral molecular geometry and is similar to that found previously for steric interactions

Quantum Theory of Chiral Interactions in Cholesteric Liquid Crystals

The effective chiral interaction between molecules arising from long-range quantum interactions between fluctuating charge moments is analyzed in terms of a simple model of chiral molecules. This model is based on the approximations that (a) the dominant excited states of a molecule form a band whose width is small compared to the average energy of excitation above the ground state and (b) biaxial orientational correlation between adjacent molecules can be neglected. Previous treatments of quantum chiral interactions have been based on a multipole expansion of the effective interaction energy within second-order perturbation theory. We consider a system consisting of elongated molecules and, although we invoke the expansion in terms of coordinates transverse to the long axis of constituent molecules, we treat the longitudinal coordinate exactly. Such an approximation is plausible for molecules in real liquid crystals. The macroscopic cholesteric wave vector Q (Q=2π/P, where P is the pitch) is obtained via Q=h/K2, where K2 is the Frank elastic constant for twist and h is the torque field which we calculate from the effective chiral interaction κIJaI×aJ⋅RIJ, where the unit vector aI specifies the orientation of molecule I and RIJ is the displacement of molecule I relative to molecule J. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. When both molecules are excited, we regain the RIJ−8 dependence of κIJ on intermolecular separation found previously by Van der Meer et al. [J. Chem. Phys. 65, 3935 (1976)]. The two-molecule, unlike the one-molecule term, can be interpreted in terms of a superposition of pairwise interactions between individual atoms (or local chiral centers) on the two molecules. Contributions to κIJ when one molecule is excited in the virtual state are of order RIJ−7 for helical molecules which are assumed not to have a global dipole moment, but whose atoms possess a dipole moment. It is shown that for a helical molecule Q can have either the same or the opposite sign as the chiral pitch of an individual molecule, depending on the details of the anisotropy of the atomic polarizability. The one-molecule mechanism can become important when the local atomic dipoles become sizable, although biaxial correlations (ignored here) should then be taken into account. Our results suggest how the architecture of molecular dipole moments might be adjusted to significantly influence the macroscopic pitch

Lithocholic Acid Hydroxyamide Destabilizes Cyclin D1 and Induces G0/G1 Arrest by Inhibiting Deubiquitinase USP2a

USP2a is a deubiquitinase responsible for stabilization of cyclin D1 – a crucial regulatorbof cell cycle progression and a proto-oncoprotein overexpressed in numerous cancer types. Here we report that lithocholic acid (LCA) derivatives are inhibitors of USP proteins, including USP2a. The most potent LCA derivative, LCAHA, inhibits USP2a, leading to a significant Akt/GSK3β-independent destabilization of cyclin D1, but does not change the expression of p27. This leads to the defects in cell cycle progression. As a result, LCAHA inhibits the growth of cyclin D1-expressing, but not cyclin D1-negative cells independently of the p53 status. We show that LCA derivatives may be considered as future therapeutics for the treatment of cyclin D1-addicted, both p53-expressing and p53-defective cancer types

Quantum theory of cholesteric liquid crystals

A long standing and central problem in cholesteric liquid crystals is to relate the macroscopic pitch to the underlying microscopic interactions. These interactions are of two types which we call quantum (dispersion) and classical. Here we show that, contrary to common belief, intermolecular biaxial correlations usually play an important role for dispersion forces. To understand the microscopic picture of cholesteric liquid crystal we first analyze the effective chiral interaction between molecules arising front long-range quantum interactions between fluctuating charge moments in terms of a simple model of a chiral molecule. This model is based on the approximations that (a) the dominant excited states of a molecule form a band whose width is small compared to the average energy of excitation above the ground state and (b) biaxial orientational correlation between adjacent molecules can be neglected. We consider a system consisted of elongated molecules and, although we invoke the expansion in terms of coordinates transverse to the long axis of constituent molecules, we treat the longitudinal coordinate exactly. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. The two-molecule interaction can be interpreted in terms of a superposition of pairwise interactions between individual atoms (or local chiral centers) on a chiral molecule and centers of anisotropic part of polarizability on the other molecule, while the one-molecule term involves three-body interactions between two local dipole moments of a chiral molecule and centers of anisotropic part of polarizability on the other, possibly nonchiral molecule. The numerical estimates of the pitch appeared from the above mechanism even without the Taylor expansion of the potential turns out to be considerably larger than experimental results and so it appears that the mean field treatment of these interactions can be used only in rare cases. However when rather than spinning each molecule, we allow for biaxial correlations between molecular orientations, then we find a cholesteric pitch close to the experimentally observed one. In the presence of biaxial correlations the molecular parameters which determine the cholesteric pitch are different from these in the absence of biaxial correlations. For instance, it is shown that, contrary to the results in mean field approximation, with biaxial correlations between molecules the chiral interaction depends very weakly on anisotropic part of molecular polarizability. Finally, with experimental data in mind, we treat the cholesteric liquid crystal consistent of PBLG (poly-γ-benzyl-L-glutamate) molecules. In agreement with above statement we find that the cholesteric pitch P is determined by the character of intermolecular correlations. (Abstract shortened by UMI.

Inter-temporal asset pricing in general equilibrium with arbitrage opportunities

This thesis develops general equilibrium with arbitrage opportunities and considers its asset pricing implications. We show numerically that if the trading of the stock and its derivative is constrained then a general competitive equilibrium with states where Sharpe ratios of two risky securities are different can exist. We characterize asset prices in such an equilibrium and show that it admits arbitrage opportunities for a price taking speculator. If the equilibrium does not admit states with arbitrage, then the derivative always costs the Black-Scholes price. We show that the equilibrium approach predicts arbitrage opportunities in states of the market where the existing no-arbitrage approach for pricing a contingent claim in the market with frictions does not. To identify all arbitrage opportunities we introduce the upper and lower hedging portfolios of the derivative which contain the derivative itself. We find the states in which the values of hedging portfolios are different and show that these states allow a free lunch. Finally we show that a speculator with a finite risk aversion prefers more risk exposure instead of taking maximal position in arbitrage. Moreover, while an arbitrageur has a choice between investing into risky and riskless arbitrage he will always trade only riskless arbitrage

Quantum theory of cholesteric liquid crystals

A long standing and central problem in cholesteric liquid crystals is to relate the macroscopic pitch to the underlying microscopic interactions. These interactions are of two types which we call quantum (dispersion) and classical. Here we show that, contrary to common belief, intermolecular biaxial correlations usually play an important role for dispersion forces. To understand the microscopic picture of cholesteric liquid crystal we first analyze the effective chiral interaction between molecules arising front long-range quantum interactions between fluctuating charge moments in terms of a simple model of a chiral molecule. This model is based on the approximations that (a) the dominant excited states of a molecule form a band whose width is small compared to the average energy of excitation above the ground state and (b) biaxial orientational correlation between adjacent molecules can be neglected. We consider a system consisted of elongated molecules and, although we invoke the expansion in terms of coordinates transverse to the long axis of constituent molecules, we treat the longitudinal coordinate exactly. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. The two-molecule interaction can be interpreted in terms of a superposition of pairwise interactions between individual atoms (or local chiral centers) on a chiral molecule and centers of anisotropic part of polarizability on the other molecule, while the one-molecule term involves three-body interactions between two local dipole moments of a chiral molecule and centers of anisotropic part of polarizability on the other, possibly nonchiral molecule. The numerical estimates of the pitch appeared from the above mechanism even without the Taylor expansion of the potential turns out to be considerably larger than experimental results and so it appears that the mean field treatment of these interactions can be used only in rare cases. However when rather than spinning each molecule, we allow for biaxial correlations between molecular orientations, then we find a cholesteric pitch close to the experimentally observed one. In the presence of biaxial correlations the molecular parameters which determine the cholesteric pitch are different from these in the absence of biaxial correlations. For instance, it is shown that, contrary to the results in mean field approximation, with biaxial correlations between molecules the chiral interaction depends very weakly on anisotropic part of molecular polarizability. Finally, with experimental data in mind, we treat the cholesteric liquid crystal consistent of PBLG (poly-γ-benzyl-L-glutamate) molecules. In agreement with above statement we find that the cholesteric pitch P is determined by the character of intermolecular correlations. (Abstract shortened by UMI.