Liang Chen, (ARC, Heriot Watt University)

Title: Sampling variation and its impact on the calibration of stochastic mortality models.


This talk considers the impact of sampling variation on the calibration of stochastic mortality models. Random variation in deaths counts results in parameter uncertainty in estimates of age, period and cohort effect in the model. In turn this has an impact on time series parameter estimates.

With small populations, sampling variation causes an upwards bias in the estimated volatility of period effects using standard maximum likelihood methods. We seek to counteract this problem of bias using Bayesian inference.

We use England and Wales (EW) males as a benchmark and then scale this down to simulate small populations. We will discuss to what extent Bayesian methods reduce bias in the model volatility, using full EW population as a benchmark.

Marcus C. Christiansen, (Heriot-Watt University)

Title: Decomposing life insurance liabilities into risk factors


The decomposition of (life) insurance liabilities into risk factors associated with various sources of risk such as equity, interest, or mortality is of great relevance in view of risk management and product design. Nevertheless, although several decomposition approaches have been proposed, no systematic analysis is available. The presentation shows how to close that gap by introducing properties for meaningful risk decompositions and demonstrating that existing approaches violate at least one of these properties. As an alternative, we propose a novel MRT decomposition that relies on martingale representation and show that it satisfies all of the properties. We discuss its calculation and present a detailed example illustrating its applicability.

Dominic Cortis, (University of Leicester)

Title:Betting Markets: Limitations and Reserving


The betting industry has been traditionally been researched as it represent the financial markets in microcosm. However the industry has grown significantly – yet there have been no developments in creating a regulatory framework akin to the EU Solvency and Capital Requirement Directives in the Financial Services. This presentation will describe how an odd is set together with the limitations posed on bookmakers. Moreover a modular method to calculate the profit and variance of a portfolio of wagers placed with a bookmaker by subdividing these into bundles according to their likelihood size.

Dr. Adrian O. Hagan, (UCD, Dublin)

Title: Actuarial Risk Matrices: The Nearest Positive Semidefinite Matrix Problem


Actuarial risk correlation matrices are often constructed using output from disparate modelling sources and can also be adjusted using subjective judgment - for example increasing the estimated correlation between two risk sources in order to confer reserving prudence as to potential insurance losses from both sources simultaneously. Hence, while individual elements still obey the necessary assumptions of correlation values, the resultant correlation matrix is often not mathematically valid in the sense that it is not positive semidefinite and hence cannot be inverted. This can prove very problematic in using the matrix in statistical models, for example in the commonly used multivariate Gaussian density function.

This paper explores methods that allow actuaries to identify the nearest symmetric positive semi-definite matrix to a given initial invalid symmetric correlation matrix. The methods are adapted to adhere to the necessary assumptions underpinning a correlation matrix (namely symmetry and that all elements are between -1 and +1 inclusive). The problem is further finessed by considering imposition of a block structure on the initial correlation matrix. This commonly employed technique identifies off-diagonal subsets of the correlation matrix where values can or should all be set equal to some constant; due to similarity in the nature of the underlying risks and/or with the goal of increasing computational efficiency for processes involving very large matrices.

The problem is initially explored using two mathematical matrix programming approaches:Semidefinite Programming (SDP) and the Alternating Projections Method (APM). Both approaches are adapted to allow implementation of further linear constraints (such as the off-diagonal blocks of fixed values) beyond the classical nearest positive semidefinite matrix problem. "Nearness'' is primarily considered in terms of two summary measures for differences between matrices: the Lowest Maximum (Chebychev) Norm and the Frobenius Norm. It is shown that APM is extremely efficient in producing solutions with minimum Frobenius norm but that both SDP and APM fail to converge to matrices with the least maximum norm. However they can be used to prove the existence of matrices with lower maximum norms than those obtained by default. For this reason, further approaches including the Shrinking Method are explored to provide solutions with the smallest possible maximum norm. Convergence speeds for the various approaches implemented are calculated and compared and sample data and accompanying MATLAB code for implementation of the methods is provided for the reader's convenience.

All methods considered are demonstrated to work well both on artificial correlation matrices and on real actuarial risk matrices provided as part of a collaboration with Tokio Marine Kiln (TMK). Ultimately the Alternating Projections Method is identified as being superior in terms of the Frobenius norm as it can be demonstrated to work well across the full range of problems considered and is also optimal in terms of convergence speed. The Shrinking Method, building on the output of the APM algorithm, is demonstrated to provide excellent results at low computational cost for minimizing the Chebychev norm.

Web Link: A link to the complete submitted research paper will be available from the end of May

Zhaoxun Mei, (ARC, Heriot Watt University)

Title: Optimal design of structured products


The project aims to design new products that can be used by insurance companies to smooth investment returns for their customers.

The focus is on new mechanisms for investment risk sharing between customers, and between customers and the insurance company. The project will involve stochastic models for financial markets, stochastic optimization techniques and application of economic theory on inter-generational risk sharing

This paper introduces a new product which is inspired by an existing pension product in Denmark examined by Guillen, Jorgenson and Nielsen (2006). Some characteristics of this product is given first. The pricing and hedging of this product is presented in part 2. In the last part, some investigations of this product is discussed. The comparisons between these two products under Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT) are given in the third part. Some investigation of this product under CPT shows the demand of guarantees from customers depend on the length of their investment windows.

Carmen Boado Penas, (IFAM, University of Liverpool)

Title: Linking PAYG pensions to life expectancy: A solution to guarantee long-term sustainability?


The aim of this paper is twofold. Firstly, using nonlinear optimization, it seeks to assess whether a sustainability factor linked to life expectancy is sufficient to guarantee the financial stability in a generic PAYG pension system. Secondly, considering different sustainability factors, it designs different optimal strategies, that involve variables such as the contribution rate, age of retirement and/or indexation on pensions, to restore the long-term financial equilibrium of the system. These optimal strategies, which we call automatic balancing mechanisms (ABMs), calculate the optimal path of these variables over time and absorb fluctuations in longevity, fertility rates, salary growth or any other kind of uncertainty faced by the pension system.

JEL Classification: E62, H55, J11, J26.

Keywords: Demographic change, Pay-as-you-go, Public pensions, Optimization, Risks.

Joint work with Humberto Godinez-Olivares (University of Liverpool) & Steven Haberman (Cass Business School)

Web Link: Dr. Carmen Boado Penas 

Aniketh Pittea, (ARC, University of Kent)

Title: Impact of changing population demographics on pension plans


The generation born in the 20 years following the end of World War II has had a profound impact on long-term economic growth in developed countries over the last half of the 20th century. The retirement of this “boomer” generation has the potential to continue to be a dominant economic factor. In particular, ageing populations will continue to put pressure on the benefit delivery and cost of social security systems in many developed countries. The effect will be compounded if changing population structure reduces asset returns below levels currently anticipated.

In this research, we ask: will the pension plan payments be adequate for the retirement needs of an ageing population?

We implement existing economic and demographic models in actuarial literature to quantify financial risks underlying large pension plans. This will then enable us to investigate the impact of ageing population on pension plans by incorporating models specifically designed to capture the impact of ageing on both economy and demography.

The interaction between population structure, investments and asset returns will be of interest to pension funds, actuaries and policy-makers, all of whom are interested in the overall health of both public and private pension plans.

Tracey Zalk, (Visiting Fellow, Global Sustainability Institute, Anglia Ruskin University)

Title: Industry-academic collaboration: exploring nexus shocks


In 2013 the research report, Resource Constraints: Sharing a Finite Word. Implications of limits to growth for the Actuarial Profession, commissioned by the Institute and Faculty of Actuaries and carried out by a group of academics and practitioners was launched. This report, alongside annual literature reviews led by the Institute and Faculty of Actuaries, was intended to support ongoing dialogue between the actuarial profession and the research community. The area of focus, namely trends in global resources and how these trends may impact financial risk, remains a significant challenge although increasing attention has been given to specific aspects of these risks – most notably emerging climate change risks. 

In 2014 the theme of the Actuarial Teachers and Researchers conference was bridging the gap between academia and industry with emphasis on risk models. However, many models still operate on the basis that the recent past is the best possible guide to the future. Given changes in the climate leading to shifting probabilities in extreme weather, geopolitical challenges around the supply of oil and recent global impacts of food productions shocks linked to the Arab Spring it is more important than ever that further engagement between academics and practitioners is needed. 

Two such partnerships have recently been set up to further this engagement. One, led by Lloyd’s of London, explored the risks associated with global food production and led to the publication in 2015 of the Food System Shock report. This explored the plausible direct and indirect risks associated with a global food production shock. Importantly the focus of this work was on the short term. The second example has just been launched. The new £6 million Economic and Social Research Council (ESRC) Centre for the Understanding of Sustainable Prosperity (CUSP) includes the Institute and Faculty of Actuaries as a partner. CUSP explores the transition to new economic paradigms that could potentially solve some of the biggest financial risks that we face today including inequality and environmental degradation. CUSP academics bring a wealth of experience in social, technical and political thinking and aligning this with the experience of actuaries will allow a better and more detailed view of financial risks and opportunities. 

These types of formal partnerships as well as informal collaborations allow us to better build future potential bridges and specifically we will explore direct links to Institute and Faculty of Actuaries working parties such as Climate Change, Financial Inequality and Infrastructure Investments.

Web Link: Global Resource Observatory 

Presentation - Industry-academic collaboration: exploring nexus shocks (PDF, 1.53MB)