Sh Doole

A piece wise linear suspension bridge model: nonlinear dynamics and orbit continuation

The effect of harmonic excitation on suspension bridges is examined as a first step towards the understanding of the effect of wind, and possibly certain kinds of earthquake, excitation on such structures. The Lazer-McKenna suspension bridge model is studied completely for the first time by using a methodology that has been successfully applied to models of rocking blocks and other free-standing rigid structures. An unexpectedly rich dynamical structure is revealed in this way. Conditions for the existence of asymptotic periodic responses are established, via a complicated nonlinear transcen- dental equation. A two-part Poincare map is derived to study the orbital stability of such solutions. Numerical results are presented which illustrate the application of the analytical procedure to find and classify stable and unstable solutions, as well as determine bifurcation points accurately. The richness of the possible dynamics is then illustrated by a menagerie of solutions which exhibit fold and flip bifurca...

Designing Low-Volatility Strategies

Since the Global Financial Crisis hit in 2008, low volatility has garnered increased attention from institutional investors. In this article, the authors delve into the practicalities of low-volatility investing, including construction issues, their performance in different market regimes, and the effect of recent increased demand on the strategy’s behavior. They discuss that although heuristic approaches tend to be simpler, only optimization-based approaches can take full advantage of the correlation between stocks. Constraints are essential in creating a well-behaved and investable low-volatility index. The authors show how different constraints can improve a minimum volatility strategy without having a significant impact on its volatility. Via attribution analyses, they analyze the sources of long-term outperformance of a minimum volatility index and discuss the valuation of minimum volatility indexes after the recent increases in demand and outperformance.

The bifurcation of steady gravity water waves in (R, S) parameter space

The bifurcation of steady periodic waves from irrotational inviscid streamflows is considered. Normalizing the flux Q to unity leaves two other natural quantities R (pressure head) and S (flowforce) to parameterize the wavetrain. In a well-known paper, Benjamin & Lighthill (1954) presented calculations within a cnoidal-wave theory which suggested that the corresponding values of R and S lie inside the cusped locus traced by the sub- and supercritical streamflows. This rule has been applied since to many other flow scenarios. In this paper, regular expansions for the streamfunction and profile are constructed for a wave forming on a subcritical stream and thence values for R and S are calculated. These describe, locally, how wave branches in (R, S) parameter space point inside the streamflow cusp. Accurate numerics using a boundary-integral solver show how these constant-period branches extend globally and map out parameter space. The main result is to show that the large-amplitude branches for all steady Stokes’ waves lie surprisingly close to the subcritical stream branch. This has important consequences for the feasibility of undular bores (as opposed to hydraulic jumps) in obstructed flow. Moreover, the transition from the ‘long-wave region’ towards the ‘deep-water limit’ is characterized by an extreme geometry, both of the wave branches and how they sit inside each other. It is also shown that a single (Q, R, S) triple may represent more than one wave since the global branches can overlap in (R, S) parameter space. This non-uniqueness is not that associated with the known premature maxima of wave properties as functions of wave amplitude near waves of greatest height.

Managing Risks Beyond Volatility

Minimum volatility strategies enjoy broad support in the academic literature and have been applied extensively by institutional investors to reduce portfolio volatility. In this article, the authors discuss how such strategies can adapt to address risks beyond price volatility. Specifically, concentration, sustainability, and crowding risks could be mitigated using appropriate but simple optimization constraints. However, adding a diversification constraint increased exposure to residual volatility and had a negative impact on risk reduction and risk-adjusted performance. In contrast, to help manage environmental, social, and governance (ESG) risks, adding a significant sustainability constraint had only a small effect on the risk reduction properties. Finally, introducing constraints on the value exposure ensured the market-relative valuations of the strategy remained attractive for only a small increase in realized volatility. The authors show that simple constraints could be used effectively in minimum volatility strategies to manage risks beyond volatility.

The Capacity of Factor Index Strategies: Assessment and Control

Capacity measures how much can be invested in a strategy before declining expected returns make competing strategies look more attractive. Existing approaches for measuring capacity are often based on a strategy’s expected return and hence are vulnerable to estimation error. Using the exposure characteristics of factor indexes is an alternative way of gauging the capacity pressure such strategies may be facing. This article discusses different ways of controlling investment capacity in designing a factor index. With careful design, the capacity of a factor index can be improved without significantly compromising exposure to the target factor. Six practical ways are investigated that allow investors to modify their strategies to be capacity-sensitive while still capturing the desired factor exposure: controlling the maximum benchmark multiple, trade size, and turnover and rebalance frequency, alongside the use of staggered and spread rebalancing.

Dynamic bifurcation in a system of PDES with a conserved first integral

A class of initial-boundary value problems with a conserved first integral is studied. The class of problems includes particular cases of interest. In one parameter limit, the equations arise as a similarity reduction of the Navier-Stokes equations, which has been recently studied for its blow-up properties, and in another, a class of scalar reaction-diffusion equations, modified by the addition of a non-local non-linearity to ensure conservation of the first integral. Once the problem has been stated, it is shown how it may be derived from the Navier-Stokes equations in one parameter limit. Steady-state solutions are then constructed using a rigorous iterative method which we call Crandall Iteration. The steady solution set includes, in a particular parameter limit, those of the Cahn-Hilliard equation. Amplitude expansions and centre manifold theory are employed to analyze the heteroclinic orbits connecting these steady solutions. It is proved that Hopf bifurcation of periodic solutions cannot occur