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RISK MEASUREMENT PROBLEMS IN INSURANCE MATHEMATICS


   School of Mathematics

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  Dr M. Amine Lkabous  Applications accepted all year round  Funded PhD Project (UK Students Only)

About the Project

In risk theory, a good understanding of solvency risk is of paramount importance to reduce the negative impact of periods of nancial distress. Therefore, there is a consistent need for sophisticated mathematical models and powerful probabilistic techniques for the quantification of risks. This objective of this PhD project is to address, from a mathematical perspective, risk measurement problems faced by insurance companies. More precisely, in actuarial ruin models based on stochastic processes.

The objective of this Phd proposal is twofold. First, you will study some probabilistic properties of path-dependent functionals of risk processes that are of interest for solvency risk measurement. Also, you will investigate optimal stopping and stochastic control problems related to spectrally negative Lévuy processes as in [2]. Some mathematical results obtained through this research program will be transferred to other fields of research such as actuarial finance. We propose that the candidate starts his training on Markov processes in risk theory problems using spectrally negative Lévy processes. Papers on Parisian ruin such as [6] and [1] will give a general feeling for some of the main questions. Also, analysing Parisian ruin quantities for the drawdown process is an interesting research direction. Last but not least, a possible direction for future research would be to look into other problems of interest connected to mathematical finance using exponential one-sided Lévy processes as in [4]. This proposal is addressed to candidates having a good background in Stochastic processes. For rudiments of spectrally negative Lévy processes and fluctuation identities, one may use the books of Kyprianou [5] or Bertoin [3]. A perfect candidate would be someone who did his msc project on risk theory and/or optimal stopping problems.

The successful applicant will have the opportunity to collaborate with world-leading researchers. Visiting well-known actuarial science departments in the UK, Europe or Canada would be possible. Our enthusiastic and lively group of staff, postdocs and PhD students and external collaborations, make for a stimulating research environment. We are part of the Southampton Statistical Sciences Research Institute, one of the largest and most varied groups of academic statisticians in the UK.

Requirements :

Essential qualification : Obtained (or expected) Msc (or equivalent) in Actuarial science/finance, Mathematics, Statistics or Probability.

Enquiries : For more information, contact Dr Amine Lkabous ([Email Address Removed]).


Funding Notes

Students with government/external fellowships are also welcome to apply.

References

[1] H. Albrecher, J. Ivanovs, and X. Zhou, Exit identities for Lévy processes observed at Poisson arrival times, Bernoulli 22 (2016), no. 3, 13641382.
[2] E. J. Baurdoux and J.M. Pedraza, Lp optimal prediction of the last zero of a spectrally negative lévy process, arXiv:2003.06869[math.PR] (2020).
[3] J. Bertoin, Lévy processes, Cambridge University Press, 1996.
[4] H. Guérin and J.-F. Renaud, Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view, Adv. in Appl. Probab. (2016).
[5] A. E. Kyprianou, Fluctuations of Lévy processes with applications - Introductory lectures, Second, Universitext, Springer, Heidelberg, 2014.
[6] R. L. Loeen, I. Czarna, and Z. Palmowski, Parisian ruin probability for spectrally negative Lévy processes, Bernoulli 19 (2013), no. 2, 599609.
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