School of Mathematics

Titles & Abstracts

Actuarial Teachers and Researchers Conference 2014Titles & Abstracts

Jiro Akahori (Ritsumeikan University, Japan)

Title: Parametrix of Static Hedge


A parametrix is an approximation to a fundamental solution of a PDE (as Wikipedia says) by an easier one (sometimes it is a Gaussian kernel).

We may understand it as an approximation of an option price in a general diffusion environment by a Black-Scholes one. In the latter, it is known that a perfect static replication of a barrier option is possible. I will introduce a parametrix by the static hedge in BS of barrier type options in a general diffusion environment.  I will then discuss (if I have time) some applications to insurance.

(joint work with F. Barsotti and Y. Imamura).


Daniel Alai (University of Kent)

Title: Investigating the Relationship between Socio-Economic Circumstances and Causal Mortality

Abstract: We investigate the relationship between socio-economic circumstances and causal mortality using a unique dataset obtained from the UK Office of National Statistics.

We apply a multinomial logistic framework; the reason is twofold. First, covariates such as socio-economic circumstances are readily incorporated. And second, the framework is able to handle the intrinsic dependence amongst the competing causes. As a consequence of the dataset and modelling framework, we are able to investigate the impact of improvements in cause-specific mortality by socio-economic circumstances. We assess the impact using (residual) life expectancy, a measure of aggregate mortality. Of main interest are the gaps in life expectancy amongst the socio-economic groups, the trends in these gaps over time, and the ability to identify the causes most influential in altering these gaps.

Co-authored with Severine Arnold (-Gaille), Madhavi Bajekal and Andres M. Villegas.


Andrew Cairns (Heriot-Watt University)

Title: Multi-population Mortality Modelling: A Danish Case Study

Abstract: This talk will focus on the modelling of mortality in several sub-populations of a national population. We use as a case study Danish register data that allows us to subdivide the national population into 10 equal sized groups on the basis of wealth and income. The derived data shows a clear ranking of the 10 groups over all ages and we will discuss the dynamics of the different groups.

We propose a multi-population stochastic model for forecasting mortality in the 10 groups than can be used to construct hypothetical mortality scenarios for typical pension plans.

This, then, allows us to assess the basis risk that might be inherent in an index-linked mortality hedge using national mortality as a proxy for plan mortality.


Gioel Calabrese (Hymans Robertson)

Title: Building interest rate scenarios

Abstract: Sophisticated stochastic simulation frameworks for producing economic scenarios are often part of the arsenal of quantitative risk management tools used by actuaries.  In this section I will discuss the problem of generating scenarios for nominal rates, real rates and inflation for multiple economies and the calibration of the underlying stochastic models.


Corina Constantinescu  (University of Liverpool)

Title: Summer projects

Abstract: For the last 2 years, in Liverpool, we have had summer projects for UG and MSc students in cooperation with industry. Would present some of the lesson learned and some of the future plans.


Angelos Dassios (London School of Economics)

Title: Dynamic Contagion processes

Abstract: The talk is motivated by default contagion in financial mathematics. A point process is developed to model defaults. This model is inspired by stochastic intensity models but also of branching theory. The model goes beyond Cox processes (ie process with a stochastic intensity). We will give a branching process definition and survey important results and applications to credit risk. Moreover, we will use the process as a claim arrivals process in general insurance and develop results concerning the probability of ruin. Applications of the mathematical tools developed for the case of delayed claims will also be discussed if time permits.


Catherine Donnelly (Heriot-Watt University)

Title: Are customer needs driving the retirement industry?

Abstract:  We are in the midst of a slow-burning pensions crisis.  Individuals who wish to save for their retirement are asked to assess their 'risk appetite' through an online questionnaire and then decide how much to invest in equities.  Subsequently, they receive regular statements from their fund manager showing the value of their retirement savings and their investment return over the year.

Yet the individual is generally seeking an inflation-proofed income in retirement.  They should not be asked how they should invest for retirement, as they are not financial experts.  They should be given information that has an explicit interpretation for their retirement income goals: are historical investment returns the best way to do this?  Individuals are forced into a decision-making framework that is highly confusing even to the highly-educated person.

Following an approach proposed by the Nobel Laureate Robert C. Merton, we suggest how retirement income decisions could be made by the individual in a discussion with their financial adviser.  We solve for the investment strategy that allows these income goals to be reached, by solving an optimal stochastic control problem set in a suitable financial market model.  Our approach allows the individual to understand the impact of changing their retirement income goals in an easily understood way, and removes the implicit need for them to become financial experts.

This is joint work with Montserrat Guillen (University of Barcelona), Jens Perch Nielsen (Cass Business School) and Ana Maria Perez-Marin (University of Barcelona).


Brian Fleming (Standard Life Investments)

Title: Measuring diversification and systemic risk using entropy

Abstract: Diversification is a subject often discussed but there is little agreement on how to measure it. In recent research, equivalence between diversification and entropy has been well developed in the context of portfolio risk. This has resulted in new metrics such as the effective number of bets in an investment portfolio. While this equivalence makes intuitive sense, the metrics themselves can sometimes produce unstable and counter-intuitive results. We re-examine the approach, suggest an alternative method to resolve the issues and link to existing work on systemic risk. 


Alan Forrest (The Royal Bank of Scotland)

Title: Quantifying Model Specification Risk in Practice

Abstract: In all walks of life, especially in financial institutions, models are used to help make decisions, recognising in principle the risk that a model misleads or that it supports a decision that leads to loss. Banks manage this "model risk" actively through quality assurance and validation of data and models, and by independent model review and governance. This activity can easily become top-heavy and costly, and banks need quick simple ways to quantify, prioritise and mitigate model risks. This talk outlines an approach to this problem that builds on a wide variety of theoretical developments in Statistics, Machine Learning, Information Theory and Geometry.

In the context of banking book credit risk, much model risk, especially model specification risk, can be interpreted as a "data-shift", a fundamental problem in Machine Learning that asks how much a model would need to change to fit changed data. Following developments in Geometric Statistics, pioneered by Akaike and Amari, we aim for a statement like "if the data shifts by distance x, then the model shifts by at most y". The appropriate distance is essentially Kullback's information divergence, which defines a geometry of uniform positive curvature within which model and data spaces sit orthogonally. This natural geometry mixes well with notions of entropy and model complexity to give effective bounds for model-shifts under data-shifts commonly found in banking book credit risk. This talk illustrates how this theoretical background helps us practically to prioritise model risk assessment and to quantify model sensitivities quickly without having to refit the model.


Marie Kratz  (ESSEC, Paris, France)

Title: Setting the risk appetite in presence of systemic risk

Abstract: Every financial crisis reveals the importance of systemic risk, which manifests itself by the appearance of dependence structures (that were not deemed important during normal times) and the breakdown of the diversification benefits, with, in consequence, a big impact on the risk appetite of investors. The aim of this study is to understand and point out the boundaries to risk appetite with the right choice of risk measure for settings the limits under the presence of systemic risk. To do so, we proceed via a simple stochastic modelling.


Andreas Kyprianou (University of Bath)

Title: The UK financial mathematics M.Sc.

Abstract: Postgraduate taught degrees in financial mathematics have been booming in popularity in the UK for the last 20 years. The fees for these courses are considerably higher than other comparable masters-level courses. Why? Vendors stipulate that they offer high-demand, high-level vocational training for future employees of the financial services industry, delivered by academics with an internationally recognised research reputation at world-class universities.

We argue here that, as the UK higher education system moves towards a more commercial environment, the widespread availability of the M.Sc. in financial mathematics exemplifies a practice of following market demand for the sake of income, without due consideration for the broader consequences. Indeed, we claim that, as excellent as such courses can be in intellectual content and delivery, they are mismatching needs and expectations for such education and confusing the true value of what is taught.

The story of the Mathematical Finance MSc serves as a serious case study, highlighting some of the incongruities and future dangers of free-market education.


Joseph Lo (Aspen)

Title:  Judgemental Topics in Actuarial Education and Research

Abstract: We shall explore how judgemental topics can form an integrated part of actuarial education and actuarial scientific research.  The benefits of being able to do so are conjectured to bring better job prospects for graduates and higher relevance of research insights to practitioners.  Practitioner actuaries need to use judgement when effectively working with models.  In a recent general insurance practitioner survey, large emphasis is placed on judgemental issues.  Education and research currently devote little effort and time on these topics.  The talk will highlight existing research, and argue that research in this area can also be scientific, thereby meriting a place in actuarial science research.


Douglas McLean (Moody's Analytics)

Title: Applications of Nonlinear Regression Methods in Insurance

Abstract: I consider a taxonomy of regression models that can be applied in the context of the insurance industry. We consider multiple polynomial regression, neural networks and Bayesian additive regression trees. These are applied to two problems: the nested stochastic problem and in the calibration of realistic equities models.


Adrian O'Hagan (University College Dublin, Dublin, Ireland) 

Title: Bayesian Model Averaging for Estimation of Tail Dependence in Extreme Loss Distributions)

Abstract: The use of copulas to model extreme losses and capture tail dependence is becoming increasingly common among the actuarial community. A range of parametric copulas such as the t, Joe and Gumbel copula, among others, is available for this purpose. Each copula has an accompanying form of tail dependence coefficient, which can be readily estimated from the fitted copula and the loss data supplied. However it is often unclear how to choose between competing copulas and their associated estimates of tail dependence when more than one copula provides reasonable fit to the data. Bayesian Model Averaging (BMA) provides a convenient and statistically robust solution to this problem, allowing a weighted average of the tail dependence coefficients from different copulas to be combined to form a single, blended estimate of tail dependence. The BMA process takes into account the size of the data set, the quality of copula fit (measured by its likelihood), and the complexity of each fitted copula (defined by its number of parameters). The method is illustrated and results presented for both simulated and real insurance loss data.


Andrew Smith (Deloitte)

Title: L-Moments and Financial Risk

Abstract: We develop Hosking's L-moment techniques from the properties of order statistics, contrasting the results to those found from conventional (Pearson) moments. We focus particularly on calibration of financial risk models, with applications to falls in asset prices, defaults on debts and claims on insurance policies, drawing out the merits and difficulties associated with each approach.


Pradip Tapadar (University of Kent)

Title: An economic capital study of the Pension Protection Fund and UK's defined benefit pension sector.

Abstract: With the advent of formal regulatory requirements for rigorous risk-based, or economic, capital quantification for the financial risk management of banking and insurance sectors, regulators and policy-makers are turning their attention to the pension sector, the other integral player in the financial markets. In this paper, we analyse the impact of applying economic capital techniques to defined benefit pension schemes in the UK. We propose two alternative economic capital quantification approaches, firstly for individual defined benefit pension schemes on a stand-alone basis and then for the pension sector as a whole by quantifying economic capital of the UK's Pension Protection Fund, which takes over eligible schemes with deficit, in the event of sponsor insolvency. We find that economic capital requirements for individual schemes are significantly high. However, we show that sharing risks through the Pension Protection Fund, reduces the aggregate economic capital requirement of the entire sector.


Martin White (Berkshire Hathaway)

Title: PPOs – Periodic Payment Orders

Abstract: Periodic Payment Orders (PPOs) are a commercial challenge to the long term survival of individual motor insurers, and also a regulatory and political headache.  The need for them (caring for severely injured people for the rest of their lives) is clear, and more are awarded by the courts every year.  As well as implications for the insurance industry, the impact on the future cost of the NHS is not widely understood, as PPOs are being awarded against the NHS as well.  One could therefore argue that PPOs are an "elephant in the room", both politically and commercially.

 The liabilities are ultra-long term and are pension-like in nature – a portfolio of life annuities indexed to the cost of care for group of "pensioners" with a very long combined life expectancy.  Rather than arguing "unfair", this paper presents the author’s personal view that the industry should instead provide for PPOs properly, and discusses what "properly" might mean.  The implications of this are immense, as well as technically interesting, so the scope for research is considerable.


Tracey Zalk (Global Sustainability Institute, Anglian Ruskin University)

Title: Implicit assumption underlying risk models

Abstract: Identification of countries vulnerable to resource scarcity.

Co-authored with Aled Jones, Irene Monasterolo, Victor Anderson, Alex Phillips, Julie-Anne Hogbin, Davide Natalini, Roberto Pasqualino, Efundem Agboraw, Catherine Cameron, Nick Silver and Ella Wiles.


Aihua Zhang  (University of Leicester)

Title: On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

Abstract: We study the consumption, labor supply, and portfolio decisions of a representative agent facing age-dependent mortality risk, as presented in UK actuarial life tables spanning the time period from 1951-2060 (including mortality forecasts). As in Yaari (1965) and Blanchard (1985) we assume the existence of life insurance markets. We derive closed-form solutions for optimal consumption, labor supply and investment strategy and show that the inclusion of mortality risk, and in fact the shape of the mortality risk curve as well as the various trade-offs in precautionary savings and risk taking, significantly affect the level of consumption as well as the decomposition of the investment portfolio.