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# Stochastic Modelling of Saving Accounts Linked to Stock Market

This project is to perform the stochastic and numerical analysis on the stock market linked savings accounts in order to establish the theory on the mean percentage of return (MPR).

One

27 February 2018

## Eligibility

You will hold (or expect to be awarded) a first or 2:1 UK Honours degree, or overseas equivalent, mathematics or statistics or in a sciences related subject.

## Project Details

Income needs seem to be a top priority at the moment---and with low savings rates and top UK equity income funds yielding less than 4%, it is perhaps easy to understand why. With savings rates continuing at their record lows, some savers are turning to alternatives. It is in this spirit that many financial institutions are offering stock market linked savings plans to those looking to combine a high yield opportunity with some protection against a falling stock market. That is why the stock market linked savings accounts have recently become very popular. The returns of these accounts are random so the returns, even the initial capital, are not guaranteed. They are very much different from the familiar fixed-term-fixed-rate savings accounts.

The aim of this PhD project is to perform the stochastic and numerical analysis on the stock market linked savings accounts in order to establish the theory on the mean percentage of return (MPR).

The MPR depends mainly on two factors:

(1) The structure of the saving accounts, namely the terms of the portfolios (plans);

(2) The behaviour of the stock market linked.

There are various portfolios in the market. This PhD project will analyze a number of typical plans. On the stochastic modelling of the stock market, there are various stochastic differential equation (SDE) models. In this project, some of these SDE models will be used. The key objective here is to establish the explicit formulas for the MPRs of the underlying stock marker linked saving accounts if possible; otherwise develop some new techniques to establish better approximation schemes.

The project will then develop the techniques of the stochastic and numerical analysis to deal with other more complicated financial derivatives including bond, fund.