arXiv subjects

James Dalby

Publications and source records attributed to James Dalby.

10 recordsLinked to original sources

arXiv2025

Machine-learning a family of solutions to an optimal pension investment problem

We use a neural network to identify the optimal solutions to a family of pension investment problems, where the parameters determining an investor's risk and consumption preferences are given as inputs to the neural network in addition to economic variables. Training a single network across such a family fails without modification. Our main contribution is a scaling of the loss function that resolves this, together with a proof that the resulting algorithm converges. We use this to develop a practical tool for exploring how pension outcomes vary with preference parameters. We use a Black-Scholes economic model so that we may validate the accuracy of the network using a classical and provably convergent numerical method developed using the duality approach.

q-fin.CP↗

arXiv2025

A study of ferronematic thin films including a stray field energy

Ferronematic materials are colloidal suspensions of magnetic particles in liquid crystals. They are complex materials with potential applications in display technologies, sensors, microfluidics devices, etc. We consider a model for ferronematics in a 2D domain with a variational approach. The proposed free energy of the ferronematic system depends on the Landau-de Gennes (LdG) order parameter $\mathbf{Q}$ and the magnetization $\mathbf{M}$, and incorporates the complex interaction between the liquid crystal molecules and the magnetic particles in the presence of an external magnetic field $\mathbf{H}_{ext}$. The energy functional combines the Landau-de Gennes nematic energy density and energy densities from the theory of micromagnetics including (an approximation of) the stray field energy and energetic contributions from an external magnetic field. For the proposed ferronematic energy, we first prove the existence of an energy minimizer and then the uniqueness of the minimizer in certain parameter regimes. Secondly, we numerically compute stable ferronematic equilibria by solving the gradient flow equations associated with the proposed ferronematic energy. The numerical results show that the stray field influences the localization of the interior nematic defects and magnetic vortices.

math.AP↗

arXiv2025

A comparison of the effectiveness of alternative DC and CDC designs in a UK market

We use three stochastic models to evaluate the effectiveness of a number of possible pension designs which have been proposed for use in the UK. We consider individual DC schemes followed by full annuitisation and a flex-and-fix strategy which combines drawdown with gradual annuitisation. We compare these approaches with collective designs including: a flat-accrual shared-indexation CDC scheme that is similar to the Royal Mail Collective Pension Plan; a dynamic-accrual shared-indexation CDC scheme modelled on the approach considered in the DWP consultation on multi-employer CDC; and an alternative collective design based on a tontine structure. In our comparisons, we tune each strategy to give optimal performance given the stochastic model and a choice of representative risk preferences. We find the collective design based on a tontine structure consistently achieves the best performance in terms of member utility. We discuss the importance of leverage in the optimal investment strategies.

q-fin.PM↗

arXiv2024

Intergenerational cross-subsidies in UK Collective Defined Contribution (CDC) funds

We evaluate the performance and level of intergenerational cross-subsidy in flat-accrual and dynamic-accrual collective defined contribution (CDC) schemes which have been designed to be compatible with UK legislation. In the flat-accrual scheme, all members accrue the benefits at the same rate irrespective of age. This captures the most significant feature of the Royal Mail Collective Pension Plan, which is currently the only UK CDC scheme. The dynamic-accrual schemes seeks to reduce intergenerational cross-subsidies by varying the rate of benefit-accrual in accordance to the age of members and the current funding level. We find that these CDC schemes can often be successful in smoothing pension outcomes post-retirement while outperforming a defined contribution scheme followed by annuity purchase at the point of retirement. However, this out-performance is not guaranteed in a flat-accrual scheme and there is little smoothing of projected pension outcomes before retirement. There are significant intergenerational cross-subsidies in the flat-accrual scheme. These qualitatively mirror the cross-subsidies seen in existing defined benefit schemes, but we find the magnitude of the cross-subsidies is much larger in flat accrual CDC schemes. The dynamic-accrual scheme design is intended to reduce such cross-subsidies, but we find they still arise due to the approximate pricing methodology used to determine the benefits accrued by each contribution. Although the cross-subsidies tend to cancel out over time, in any given year they can be large. Thus, the benefits accrued by contributions should be calculated rigorously to reduce cross-subsidies.

q-fin.GN↗

arXiv2024

Optimal mutual insurance against systematic longevity risk

We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing condition. This enables an insurance market to be established even if the two funds face the same mortality risk, so long as they have different risk preferences. Provided the preferences of the two funds are not too dissimilar, insurance provides little benefit, implying the base scheme is effectively optimal. When preferences vary significantly, insurance can be beneficial.

q-fin.MF↗

arXiv2024

Optimal post-retirement investment under longevity risk in collective funds

We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein--Zin preferences. %and with preferences given by power utility. We compute analytic formulae for the optimal investment strategy, consumption is in discrete-time and there is no systematic longevity risk. We develop a stylised model of systematic longevity risk in continuous time which allows us to also obtain an analytic solution to the optimal investment problem in this case. We numerically solve the same problem using a continuous-time version of the Cairns--Blake--Dowd model. We apply our results to estimate the potential benefits of pooling longevity risk over purchasing an insurance product such as an annuity, and to estimate the benefits of optimal longevity risk pooling in a small heterogeneous fund.

q-fin.MF↗

arXiv2023

Solution landscapes of ferronematics in microfluidic channels

We study solution landscapes for ferronematics, i.e., a dilute suspension of magnetic nanoparticles in a nematic liquid crystal host, in a one-dimensional (1D) channel geometry. Adopting the modelling framework in Bisht et al.(2020), the admissible ferronematic configurations are modelled in terms of critical points of an appropriately defined ferronematic energy. There are two types of critical points: full critical points that exploit all degrees of freedom and order reconstruction (OR) critical points. OR critical points have polydomain structures, with the polydomains separated by domain walls. We find that ferronematic systems are typically multistable, i.e., the free energy has multiple competing stable critical points, which model potentially physically observable configurations; the multistability is not a priori obvious. Further, we discover multiple stable and unstable OR solutions that differ in the locations and multiplicity of domain walls. The domain walls can act as binding sites in equilibrium processes and rafts for guided transport phenomena in non-equilibrium processes.

cond-mat.soft↗

arXiv2023

A Multi-Faceted Study of Nematic Order Reconstruction in Microfluidic Channels

We study order reconstruction (OR) solutions in the Beris-Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of physical interest. We show that OR solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. We prove the existence of unique, symmetric and non-singular nematic profiles, for boundary conditions that do not allow for OR solutions. We compute asymptotic expansions for OR-type solutions for passive flows with non-constant velocity and pressure, and active flows, which shed light into the internal structure of domain walls. The asymptotics are complemented by extensive numerical studies that demonstrate the universality of OR-type structures in static and dynamic scenarios.

math.AP↗

arXiv2022

Uniaxial versus Biaxial Pathways in One-Dimensional Cholesteric Liquid Crystals

Cholesteric liquid crystals exhibit great morphological richness of static metastable states. Understanding the transitions between such states is key for the development of switchable devices. We show, using a quasi-one-dimensional model, that cholesterics exhibit distinct uniaxial and biaxial pathways between distinct minima. We study transitions between different layer numbers and prove, and show, that transition states are distinguished either through splay-mediated untwisting, understood through contact topology, or the presence of biaxiality. Furthermore we characterise a menagerie of additional saddle points that dictate the connectivity of the solution landscape.

cond-mat.soft↗

arXiv2021

One-dimensional ferronematics in a channel: order reconstruction, bifurcations and multistability

We study a model system with nematic and magnetic orders, within a channel geometry modelled by an interval, $[-D, D]$. The system is characterised by a tensor-valued nematic order parameter $\mathbf{Q}$ and a vector-valued magnetisation $\mathbf{M}$, and the observable states are modelled as stable critical points of an appropriately defined free energy. In particular, the full energy includes a nemato-magnetic coupling term characterised by a parameter $c$. We (i) derive $L^\infty$ bounds for $\mathbf{Q}$ and $\mathbf{M}$; (ii) prove a uniqueness result in parameter regimes defined by $c$, $D$ and material- and temperature-dependent correlation lengths; (iii) analyse order reconstruction solutions, possessing domain walls, and their stabilities as a function of $D$ and $c$ and (iv) perform numerical studies that elucidate the interplay of $c$ and $D$ for multistability.

math.AP↗