Financial/Actuarial Mathematics and Data Analysis

The statistical processes underlying modern finance generate challenges to both commercial and academic communities. The Finance and Actuarial Group seeks to provide insight into these processes, accompanied by the development of innovative techniques and computational tools.

Current research interests include: optimal stopping of Levy processes, option pricing, credit risk models, portfolio optimization, measures of risk and deviation, advance data analysis, advance data analysis, dimensionality reduction, principal graphs and manifolds, approximation theory, statistical methodologies and applications in actuarial science, and the financial applications of optimal stochastic controls.

Current members 

Some recent publications

Svetlana Boyarchenko and Sergei Levendorskiĭ, Non-remorse principles for real options, SIAM J Control and Optimization , 49:5 (2011), 2062-2082

Svetlana Boyarchenko and Sergei Levendorskiĭ, Pricing American Options in Regime-Switching Models, SIAM J Control and Optimization  48 (2009), pp.1353-1375

Oleg Kudrayvtsev and Sergei Levendorskiĭ, Fast and accurate pricing of barrier options under Lévy processes,  Finance and Stochastics, 13:4 (2009), pp.531-562

Sergei Levendorskiĭ, American and European Options in Multi-Factor Jump-Diffusion Models, Near Expiry, Finance and Stochastics, 12:4 (2008), pp. 541-560

A.N. Gorban, A. Zinovyev. Principal manifolds and graphs in practice: from molecular biology to dynamical systems, International Journal of Neural Systems, Vol. 20, No. 3 (2010) 219–232

A.N. Gorban, E.V. Smirnova, T.A. Tyukina, Correlations, risk and crisis: From physiology to finance, Physica A, Vol. 389, Issue 16, 2010, 3193-3217. Number 9 in the Top Hottest Articles in the Journal, April to June 2010

Gorban A.N., Gorban P.A., Judge G. Entropy: The Markov Ordering Approach. Entropy. 2010; 12(5):1145-193. http://arxiv.org/pdf/1003.1377v4.pdf

Optimal stopping for processes with independent increments, and applications, G. Deligiannidis, H. Le and S. Utev, J. Appl. Probab. Volume 46, Number 4 (2009), 1130-1145

An asymptotic variance of the self-intersections of random walks, G. Deligiannidis,  S. Utev, Sib. Math. J. Vol 52, No 4, 639-650, arXiv:1004.4845v1.

Grechuk, B., Molyboha, A., Zabarankin, M., "Mean-Deviation Analysis in the Theory of Choice". "Risk Analysis", accepted, published online http://onlinelibrary.wiley.com/doi/10.1111/j.1539-6924.2011.01611.x/abstract

Grechuk, B., Molyboha, A., Zabarankin, M., "Cooperative Games with General Deviation Measures", "Mathematical Finance", accepted, published online http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9965.2011.00495.x/abstract

Grechuk, B., Zabarankin, M., "Schur Convex Functionals: Fatou Property and Representation", "Mathematical Finance", accepted, published online http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9965.2010.00464.x/abstract

Taeryon Choi, J.Q. Shi and Bo Wang. A Gaussian process regression approach to single index model. Journal of Nonparametric Statistics 23, 21-36, 2011.

Presentation slides
A.N. Gorban, Geometry of data sets, an invited talk given at ESOF2010 (Euroscience Open Forum, Torino, July 2-7, 2010)

Teaching applets
The online Data Mining course (in preparation). K-means and K-medoids applet  and kNN and Potential energy applet

PhD students (current and some recently completed)

Grants

NSF grant #DMS-0631628, "Firm dynamics with exogenous and endogenous regime shifts", Oct 2006-Oct 2008, PI S. Boyarchenko
PhD studentship grant, funded by Institute and Faculty of Actuaries and College of Science and Engineering of the University of Leicester, 2012

Contacts

Members of our group have established contacts with the following companies:
Deloitte
Bioscreen
DeMontfort
Piran
Northamptonshire Police