# David Siska

## Contact Details

School of Mathematics, University of Edinburgh

Room 4611, JCMB, King's Buildings

Tel. 0131 651 9091

Email. d.siska@ed.ac.uk

## PhD projects

Students interested in working on a PhD project (to start in September 2019) in the areas of:

- stochastic partial differential equations,
- non-linear partial differential equations,
- stochastic control theory,
- computational methods and applications of the above (in engineering, biology, finance, ...)

See the School PhD applications website for more details regarding applications. Funding is available either through the School or via the Maxwell Institute Graduate School in Analysis and Applications (MIGSAA).

## Events

Here are some events I am (or was) helping to organize.

- Maxwell Institute Probability Day: 13th May 2016.
- Conference on Stochastic Analysis in Honor of Istvan Gyöngy's 65th Birthday: 10th-12th September 2016.
- International Workshop on BSDEs, SPDEs and their Applications: 3rd-7th July 2017.

## Preprints

- With W. Hammersley and L. Szpruch, McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions (2018).
- With Neelima, $L^p$-estimates and regularity for SPDEs with monotone semilinearity (2017).
- With Neelima, Coercivity condition for higher order moments of nonlinear SPDEs and existence of solution under local monotonicity, Submitted (2016).

## Publications

- With I. Gyöngy, Itô Formula for Processes Taking Values in Intersection of Finitely Many Banach Spaces, Stoch. PDE: Anal. Comp., 5(3), 428-455, 2017.
- With E. Emmrich, Nonlinear stochastic evolution equations of second order with damping, Stoch. PDE: Anal. Comp., 5(1), 81-112, 2017. (arXiv version).
- With I. Gyöngy and S. Sabanis, Convergence of tamed Euler schemes for a class of stochastic evolution equations, Stoch. PDE: Anal. Comp., 4(2), 225-245, 2016.
- With E. Emmrich and A. Wroblewska-Kaminska, Equations of second order in time with quasilinear damping: existence in Orlicz spaces via convergence of a full discretisation, Math. Methods Appl. Sci., 39(10), 2449-2460, 2016. (preprint version).
- With E. Emmrich and M. Thalhammer, On a full discretisation for nonlinear second-order evolution equations with monotone damping: construction, convergence, and error estimates, Found. Comput. Math. 2015
- With E. Emmrich, Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization, J. Diff. Eq., 255 (2013), no. 10, 3719-3746
- With E. Emmrich, Full discretization of the porous medium/fast diffusion equation based on its very weak formulation , Commun. Math. Sci., 10 (2012), no. 4, 1055-1080
- Error estimates for finite difference approximations of American put option price, CMAM, 12 (2012), no. 1, 108-120
- With E. Emmrich, Full discretization of second-order nonlinear evolution equations: strong convergence and applications to elasticity theory, CMAM, 11 (2011), no. 4, 441-459
- With I. Gyöngy, On Finite-Difference Approximations for Normalized Bellman Equations, Appl. Math. Optim., 60 (2009), no. 3, 297-339
- With I. Gyöngy, On Randomized Stopping, Bernoulli, 14 (2008), no. 2, 352–361

## Other

- PhD. Thesis: Numerical approximations of stochastic optimal stopping and control problems
- MSc. Thesis: Stochastic Differential Equations Driven by Fractional Brownian Motion – a White Noise Distribution Theory Approach

## Teaching

- I am supervising student projects for the MSc in Computational and Financial Mathematics and MSc in Financial Modelling and Optimization.
- In 2017/18 I am teaching Stochastic Control and Dynamic Asset Allocation.

## Numerical Computation Output Examples

- The solution of a stochastic Ginzburg-Landau equation in one spatial dimension using a newly developed Tamed Euler scheme (see related article)

- The payoff of an American put option, obtained using finite difference method, with the optimal exercise boundary indicated and a sample path of the price process (see related article)

- In 2017/18 I was one of the team teaching OOPA (materials on Learn).
- In 2017/18 I was one of the team teaching SMSTC Foundations of Probability for PhD students.
- In 2016/17 I taught Monte Carlo Methods and Simulation.
- In 2016/17 taught Risk Neutral Asset Pricing.
- In 2016/17 taught Object-Oriented Programming with Applications .
- In 2016/17 I was one of the team teaching SMSTC Probability I for PhD students.
- In 2015/16 I taught Risk Neutral Asset Pricing.
- In 2015/16 I taught Object-Oriented Programming with Applications .
- In 2015/16 I was one of the team teaching SMSTC Probability I for PhD students.
- In 2014/15 I taught Risk Neutral Asset Pricing (requires UoE login).