The 2nd Stochastics and Actuarial - Liverpool, Leeds and York Workshop

One-day workshop on stochastic processes, actuarial and financial mathematics between Liverpool, Leeds and York.

This online workshop is the second edition of a new and exciting transpennine research network in stochastic processes, actuarial and financial mathematics between the University of Liverpool, the University of Leeds and the University of York.

The aims of the 'SALLY' workshop are to provide a platform for researchers (academics and PhD students alike) to present their latest findings in a friendly and supportive environment, discuss state-of-the-art and innovative advances and, hopefully, develop new collaborations across three prominent Northern research institutions.

The workshop is open to everyone. It will take place via Zoom. If you are interested in participating, please contact Dr. Lanpeng Ji (l.ji@leeds.ac.uk) for the Zoom information.

Schedule

10.50 – 11.00am (Introduction)

11.00 - 11.45am (Dr Raghid Zeineddine - Variable annuities in a Levy based hybrid model with surrender risk)

11.45 - 12.30pm (Prof Jacco Thijssen - Optimal abandonment under a spectrally negative Levy process) 

12.30 - 1.30pm (Lunch break)

1.30 - 1.50pm (Andrea Bovo - The value of zero-sum games of controller/stopper type: a variational approach) 

1.50 - 2.10pm (Kira Henshaw - Subsidising inclusive insurance to reduce poverty)

2.10 - 2.30pm (Dr Alexandra Dias - On the adjustment of the marginal empirical distribution function when estimating the dependence parameter of a copula model)

2.30 - 2.45pm (Coffee break)

2.45 - 3.30pm (Dr Jan Palczewski - Automatic model training under restrictive time constraints)

3.30pm (Closing remarks/discussions)

Abstracts

Raghid Zeineddine (Liverpool)

Title: Variable annuities in a Levy based hybrid model with surrender risk.

Abstract: I will speak in this talk about some type of insurance products called Variable Annuities (VAs). VAs include three features: a guaranteed minimum accumulation benefit, a surrender benefit, and a death benefit. We focused in our study on the policyholder behavior towards surrender and its impact on the price of the contract. 

Jacco Thijssen (York)

Title: Optimal Abandonment under a Spectrally Negative Levy Process

Abstract: This paper considers an abandonment problem in which the underlying uncertainty is modelled as a spectrally negative L\'{e}vy jump diffusion. We show that the solution to the corresponding optimal stopping problem may not be a threshold policy found by the usual ``value-matching'' and ``smooth-pasting'' conditions. We show that smooth pasting may fail when the jumps are (in expectation) large and/or frequent. We provide a verification theorem for such cases in terms of viscosity solutions to the Hamilton--Jacobi--Bellman equation.  

Andrea Bovo (Leeds)

Title: The value of zero-sum games of controller/stopper type: a variational approach

Abstract: We consider a 2-player zero-sum game between a controller and a stopper. The game’s payoff consists in a terminal cost, a running cost and an action cost. The dynamics of the underlying process X is given by a solution of a d-dimensional controlled stochastic differential equation. The maximiser in the game can choose the time at which the game ends, whereas the minimiser can choose the control pair that affects the process X. The value function of the game is related to a variational inequality with two constraints -- an obstacle constraint and a gradient constraint. The solution of the variational inequality is found as the limit function of a sequence of solutions of penalised variational inequalities. Properties of these solutions are proved with both probabilistic and analytic approaches.

Kira Henshaw (Liverpool)

Title: Subsidising inclusive insurance to reduce poverty

Abstract: Poverty trapping refers to the event in which an entity falls below the poverty line and into the area of poverty, from which they cannot escape without external help. Considering a compound Poisson-type model for household capital, in this talk, the probability of a household falling below the poverty line (the household trapping probability) will be presented. Considering the impact of inclusive insurance (or microinsurance) as a solution for the low- and lower-middle-income populations close to the poverty line, trapping probabilities will be presented under varying structures of microinsurance, where risk theory techniques are used to obtain the explicit probabilities. Observing that microinsurance alone is not sufficient in reducing the trapping probability of specific groups of households, we instead propose a barrier strategy for government supported premium subsidies.

Alexandra Dias (York)

Title: On the adjustment of the marginal empirical distribution function when estimating the dependence parameter of a copula model

Abstract: A commonly used method for estimating dependence parameters in copula models is maximum pseudo-likelihood. It has been shown that despite its good asymptotic properties, this estimation method does not perform well when compared with methods of moments estimators for small and weakly dependent samples. Here we show that by changing the adjustment on the empirical distribution function the performance of the maximum pseudo-likelihood estimator can be improved, surpassing the performance of the methods of moments estimators. For now, this study is focussed on the Clayton copula model.

Jan Palczewski (Leeds)

Title: Automatic model training under restrictive time constraints

Abstract: Machine learning algorithms require tuning of hyperparameters which significantly affect their training and resulting accuracy. We develop a hyperparameter optimisation algorithm, which balances the quality of a model with the computational cost required to tune it. The relationship between hyperparameters, model quality and computational cost must be learnt and this learning is incorporated directly into the optimisation problem which is a mixed stochastic optimal control-stopping problem with partial information. At each training epoch, the algorithm decides whether to terminate or continue training, and, in the latter case, what values of hyperparameters to use. The performance of our algorithm is verified on a number of machine learning problems encompassing random forests and neural networks.

This talked is based on a joint work (arXiv:2104.10746) with Lukas Cironis and Georgios Aivaliotis.