# Gaussian approximations with applications to retirement products

### This project is no longer listed on FindAPhD.com and may not be available.

Dr Thomas Bernhardt  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

There is an ongoing retirement crisis in the world. Governments and insurance companies are searching for retirement products that cope with rising life expectancy and uncertain financial markets. New retirement products adjust retirees' income with experienced mortality rates and financial returns. However, that means that the retiree bears all the risk. Predicting how long the retiree receives a stable income is crucial.

Imagine a group of people who pool their funds together. Each member receives an income from the funds in the pool. The income payments depend on the remaining lifetimes of the people that form a sequence of independent random variables. Now, Donsker's theorem tells us that we can approximate such a pool with a Gaussian process. In particular, we can give asymptotic answers to questions like how long will the income of the retirees stays within given bounds. However, people differ according to age, mortality rates, savings and more. The interesting mathematical questions that follow are how to incorporate the differences. How to get robust results that can cope with the uncertainty of mortality rates? How to deliver a stable income to retirees?

We aim to find mathematical robust answers (that could be used by governments to regulate the retirement market). We focus on mortality risk. We will model the differences between individuals with mortality distributions. We will develop a mathematical theory on the space of those distributions tailed to new retirement products.

Expected Outcome:

The successful applicant will develop mathematical tools for new retirement products.

That includes but is not limited to:

1) developing a suitable distance on distributions to bound the impact of mortality heterogeneity in retirement funds,

2) developing a dynamical description of lifetables as a measure-valued process with applications to retirement funds.

The ideal candidate has a strong background in probability theory (e.g. has studied measure theory, Donsker's Theorem, and stochastic processes).

Knowledge of actuarial science is an advantage but not essential.

Review Process:

We will invite shortlisted candidates to a Zoom interview, which takes place at the end of January. One to two weeks before the interview, candidates will be emailed an exercise to solve typical for an advanced probability course. The interview questions will focus on the candidate's attempt/solution. We are most interested in the candidate's mathematical ability to prove a statement accurately.

Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.

We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).

How to apply - Department of Mathematics - The University of Manchester

## Funding Notes

This is a funded PhD studentship, covering fees and stipend (£17,668 in 2022-23). Open to all applicants.
##### Search suggestions

Based on your current searches we recommend the following search filters.

##### PhD suggestions

Based on your current search criteria we thought you might be interested in these.