Applied Probability section meeting: Stochastic processes in finance and beyond

On the afternoon of Thursday 23 May, the Applied Probability section held a workshop on ‘Stochastic processes in finance and beyond’ at the International Centre for Mathematical Sciences in Edinburgh. This meeting was held in conjunction with a week-long visit of Prof Søren Asmussen (Aarhus University) to deliver the LMS Invited Lectures 2019, on advanced topics in life insurance mathematics.

This half-day workshop brought together experts in various aspects of stochastic process theory, including researchers in applied probability and in actuarial science. Participants included several early-career researchers who were attending Professor Asmussen’s week-long lecture course.

The first talk was given by Dr Ronnie Loeffen (University of Manchester) on the topic of ‘Surplus processes with tax’, outlining a new approach to tax processes, based on an equivalence between two types of tax processes and exploiting features of the underlying Markov chain.

This was followed by a talk from Dr Burak Buke (University of Edinburgh) on ‘Many-server queues with random service rates’. Motivated by models for customer contact centres, Dr Buke presented work on multi-server queueing models in which the service rates are independent observations from a given distribution. The work focuses on large-scale limiting behaviour and the corresponding fairness of the system.

Following a break for tea, coffee and discussion between participants, Dr A Ganesh (University of Bristol) gave a talk on ‘Large deviations for Cox processes and Cox/G/¥ queues’. A biological model for protein synthesis by RNA motivates this study of a queueing system whose input is a Cox process (that is, a Poisson process with random rate). This work gives large deviations results for such a model, which apply to infinite-server queues in series.

The final talk was given by Professor Søren Asmussen on ‘Some applications of phase-type distributions to life insurance’. This talk exhibited the power and wide applicability of phase-type distributions in actuarial science, building from graduate-level material that Professor Asmussen had presented as part of his lecture course earlier in the week to the current state of the art in this area.

These four fascinating presentations showcased a variety of applications of modern stochastic process theory, and stimulated discussions both within and between these diverse application areas.

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