1. Conformal Euler-Lagrangian Equations on 4-Walker Manifolds

   Zeki Kasap

   Abstract: The main purpose of the present paper is to study almost paracomplex structures conformal Euler-Lagrangian equations on 4-dimensional Walker manifolds. A Walker nmanifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r  ≤ n/2. It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. In this study, we present complex analogues of Lagrangian mechanical systems on 4-Walker manifold. Also, the geometrical-physical results related to complex mechanical systems are also discussed for conformal Euler-Lagrangian equations..

   Keywords: Walker Manifolds, Holomorphic, Symplectic Geometry, Conformal Geometry, Lagrangian, Mechanical System, Riemannian Manifold, Almost Complex Manifolds.

   Pages: 1 – 17 | Full PDF Paper

2. Measuring Gap Risk for Constant Proportion Portfolio Insurance Strategies in Uncertain Markets

   Frank Ranganai Matenda, Eriyoti Chikodza, Victor Gumbo

   Abstract: Portfolio insurance is a critical component of portfolio management. Constant proportion portfolio insurance (CPPI) is one of the most popular and widely used portfolio insurance approaches. Recent years have witnessed increased application of CPPI. The notion of CPPI limits the downside risk of a portfolio when markets are bearish whilst maintaining its upside potential when markets are bullish. The practice behind CPPI is to shift financial resources between risky and risk-free asset classes. Conceptually, the cushion plays a central role in the dynamics of CPPI. Portfolio insurance is currently based on stochastic finance theory. Probability theory recognises randomness as the only important form of indeterminacy in asset pricing. However, recent research through uncertainty theory led to the birth of uncertain finance theory. Uncertainty theory proposes that uncertainty is the only legitimate form of indeterminacy which should be taken into account in asset pricing. Therefore, it is in the best interest of this research paper to analyse portfolio insurance in uncertain markets. In continuous time diffusion models, CPPI techniques are not exposed to gap risk. However, in practical reality CPPI approaches are exposed to gap risk. To model the dynamics of CPPI, the study adopts jump-diffusion models where the value of the underlying portfolio exhibits sudden significant downward shocks. The aim of this research paper is to quantify gap risk for CPPI strategies in uncertain markets using the investment risk index. The study also analyses the relationship between a pre-determined participation rate, m, and the value of the portfolio. The importance of m in CPPI is also examined.

   Keywords: Portfolio insurance, portfolio management, probability theory, uncertainty theory, indeterminacy, randomness, uncertainty, gap risk, uncertain markets, participation rate.

   Pages: 18 – 31 | Full PDF Paper

3. On Generation of Measurable Covers for Measurable Sets Using Multiple Integral of Functions

   Otanga Levi Olwamba, Aywa Shem Omukunda, Owino Maurice Oduor

   Abstract: In this article, we formulate an n-dimensional structure of measurable covers for measurable sets. Properties such as monotonocity, countable additivity and σ-finiteness of the projective tensor product of vector measure duality are largely applied.

   Keywords: Measurable cover, Multiple integral, Vector measure duality.

   Pages: 32 – 41 | Full PDF Paper