Crossing Barriers
Problems involving hitting and stopping times are ubiquitous across financial and insurance mathematics, and as both fields have advanced and drawn in more sophisticated models, the need to advance the corresponding mathematical techniques has grown with them.
In mathematical finance, hitting- and stopping-time problems arise classically in the study of American and barrier options, but also in robust hedging, real option theory and the modelling of credit default events. In insurance, the major application is to ruin theory — often complicated by perturbations of the surplus process corresponding to dividend strategies, such as path refraction and path reflection. The aim of the workshop was to bring together academics from the finance and insurance communities to share recent advances in the techniques connected to hitting and stopping problems.
The workshop was supported by the European Science Foundation, the AXA Research Fund, the ESF AMAMEF programme, Prob-L@b and the Bath Institute for Complex Systems (BICS). Scientific organisers: Alexander Cox, Andreas E. Kyprianou and Kees van Schaik.
Confirmed main speakers
- Hansjörg Albrecher
- Peter Carr
- David Hobson
- Dilip Madan
- Martijn Pistorius
- Hans-Peter Schmidli
Programme
All talks took place in Room 6W 1.2; refreshments and lunch were in Room 6W 1.24.
Thursday 14th January
| 10:30-11:00 | Refreshments |
| 11:00-11:05 | Welcome |
| 11:05-11:50 | Hansjörg Albrecher — Crossing Ruin Boundaries |
| 11:55-12:25 | Mihail Zervos — π-options |
| 12:30-13:30 | Lunch |
| 13:30-14:15 | Martijn Pistorius — Continuously monitored barrier options under Markov processes |
| 14:20-14:50 | Alex Mijatovic — Convergence rates for the two-sided first-passage densities |
| 14:55-15:25 | Jean-Francois Renaud — De Finetti's optimal dividends problem with a Gerber-Shiu function |
| 15:30-16:00 | Refreshments |
| 16:00-16:30 | Peter Tankov — Pricing and hedging gap risk |
| 16:35-17:05 | Alexey Kuznetsov — Wiener-Hopf factorization: an analytical approach |
| 17:10-17:40 | Griselda Deelstra — Vanna-Volga methods applied to FX derivatives: from theory to market practice |
| 17:45-19:00 | Wine Reception |
| 19:00-20:00 | Dinner |
Friday 15th January
| 9:30-10:00 | Sergei Levendorskii — Prices and sensitivities of barrier and first touch digital options in Lévy driven models, near barrier |
| 10:05-10:50 | Peter Carr — Static Hedging of Barrier Options on Driftless Diffusions |
| 10:50-11:20 | Refreshments |
| 11:20-11:50 | Kees van Schaik — A Wiener-Hopf Monte Carlo simulation technique for Lévy processes |
| 11:55-12:25 | Angelos Dassios — Double sided Parisian options |
| 12:30-13:45 | Lunch |
| 13:45-14:30 | Hans-Peter Schmidli — Conditional Law of Risk Processes Given that Ruin Occurs |
| 14:35-15:20 | Dilip Madan — Capital Requirements, Acceptable Risks and Profits |
| 15:25-15:55 | Refreshments |
Bursaries
A limited number of bursaries were available to research students and to participants from the former Soviet Union, Africa, or countries covered by the LMS “Scheme 5”. Bursaries went towards the cost of accommodation, reducing the registration fee.
Organisers
Organised by Alexander Cox, Andreas E. Kyprianou and Kees van Schaik, at the Department of Mathematical Sciences, University of Bath.