An algorithm for moment-matching scenario generation with application to financial portfolio optimization

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments)

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

Genericness of inflation in isotropic loop quantum cosmology

Non-perturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector is already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semi-definite potentials it is always possible to choose, without fine tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with generic occurrence of bounce at small volumes, particle horizon is absent thus eliminating the horizon problem of the standard Big Bang model.Comment: 4 pages, revtex4, one figure. Only e-print archive numbers correctedi in the second version. Reference added in the 3rd version. Final version to appear in Phys. Rev. Lett. Explanations improve

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe

Highest weight representations of the quantum algebra U_h(gl_\infty)

A class of highest weight irreducible representations of the quantum algebra U_h(gl_\infty) is constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators are explicitly written.Comment: 7 pages, PlainTe

Portfolio optimisation using risky assets with options as derivative insurance

We introduce options on FTSE100 index in portfolio optimisation with shares in which conditional value at risk (CVaR) is minimised. The option considered here is the one that follows FTSE100 Index Option standards. Price of options are calculated under the risk neutral valuation. The efficient portfolio composed under this addition of options shows that put option will be selected as part of the investment for every level of targeted returns. Main finding shows that the use of options does indeed decrease downside risk, and leads to better in-sample portfolio performance. Out-of-sample and back-testing also shows better performance of CVaR efficient portfolios in which index options are included. All models are coded using AMPL and the results are analysed using Microsoft Excel. Data used in this study are obtained from Datastream. We conclude that adding a put index option in addition to stocks, in order to actively create a portfolio, can substantially reduce the risk at a relatively low cost. Further research work will consider the case when short positions are considered, including writing call options.This work was partially supported by the Department of Mathematics, Brunel University

Roots of Unity: Representations of Quantum Groups

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases.Comment: 23 page

Spectral Decomposition of Path Space in Solvable Lattice Model

We give the {\it spectral decomposition} of the path space of the U_q(\hatsl) vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the \hatsl level $l$ integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the \hatsl level $l$ integrable representations in consequence.Comment: 27 pages, Plain Tex, epsf.tex, 7 figures; minor revision. identical with the version to be published in Commun.Math.Phy

On the domain wall partition functions of level-1 affine so(n) vertex models

We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil

Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection

Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behavior at large volume. As an application, the Bianchi IX model and its modified behavior close to its classical singularity is explored.Comment: revtex4, 36 pages, 10 figures. In version 2 the introduction is expanded, section III E is added and a paragraph on relevance of results is added in the conclusions. Refs updated, results unchanged. To appear in Class. Quant. Gravit