Dr Elena Boguslavskaya

PhD

Elena Boguslavskaya

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Job title: Daphne Jackson Research Fellow
Division: Maths
Organisation: Brunel University London
Tags: Fellowship: Daphne Jackson Fellowship, Researcher
Related theme: Mathematical sciences

Biography

I did my PhD at the university of Amsterdam under supervision of Professor Albert Shiryaev and Professor Chris Klaassen. Following the completion of my PhD, I was a University Research Fellow at City University, London.

My Fellowship

Imagine you put your money in a financial instrument (such as a stock) and observe the random movements of the price. At a certain point of time you want to sell it and keep your profit. But when is the right time, for instance, the optimal moment to stop observing and cash in?

Problems of this type may be associated with optimal stopping problems. Solving an optimal stopping problem means finding such a moment in time when stopping at that particular moment will bring solution to the optimisation problem (obtaining on average the highest profit).

The way to solve it is to find an optimal stopping region. Once we have the region, the best strategy is to stop observation and sell the stock, as soon as the stock price reaches the optimal region.

The standard way of finding this region is to solve complicated differential or even more complicated integro-differential equations. Numerical methods can be applied here, but they are computationally difficult.

The aim of my project is to show how to find the desired region, while avoiding solving complicated equations. I develop an alternative method by introducing a so-called ‘A- transform’, which, when applied to the payoff function, produces an indicator for the location of stopping.

One of the advantages of the proposed method is that A- transform can be easily generalised to the multidimensional case.

I also show how A-transform can be applied to the calculation of conditional mathematical expectations. This method is very efficient computationally.

Motivation to apply

I have realised that Daphne Jackson Fellowship is a perfect opportunity for me to get back to my research career.

Career benefit of Fellowship

The Daphne Jackson Fellowship provided me with the opportunity to fund my research and re-establish my career.

Advice for future applicants

Don't be afraid to be brave.