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Professor Saul Jacka

About Saul

My research is in many areas of probability theory with special interests in mathematical finance, stochastic processes, stochastic control, optimal stopping, conditioned processes and probability on trees and related structures.

I am Editor-in-Chief of the international journal Stochastics.

I am a Faculty Fellow at the Alan Turing Institute.

Contact me at: S.D.Jacka at warwick dot ac dot uk


I am always looking for new, good PhD students in any of the areas described above.

Currently, there are funded places (to start in October 2021) on the Centre for Doctoral Training in Mathematics and Statistics. See here for further information.

To find out more about research topics, please contact me. Here, one of my recent students talks about their work in 60 seconds.

Current PhD students

Puru Gupta

Kevin Engelbrecht

Ruiqi Liu

Recent PhDs

Sebastian Armstrong

Jun Maeda

Dominic Norgilas

Dejan Siraj

Adriana Ocejo

Amogh Deshpande

Matija Vidmar


Saul Jacka and Jun Maeda, An Optimal Stopping Problem Modeling Technical Analysis

Saul Jacka, Elena Hernandez-Hernandez and Alex Mijatovic, Martingale approach to control for general jump processes.

Saul Jacka and Matija Vidmar, On the informational structure in optimal dynamic stochastic control.

Saul Jacka and Abdel Berkaoui, On decomposing risk in a financial-intermediate market and reserving.

Recent Publications

Saul Jacka and Elena Hernandez-Hernandez, Minimising the expected commute time To appear in Stoch. Proc. & Appl. (2020)

Saul Jacka and Dominic Norgilas On the compensator in the Doob-Meyer decomposition of the Snell envelope. SIAM J. Control & Optimisation 57 (3) (2019)

Saul Jacka, Seb Armstrong and Abdel Berkaoui, On representing and hedging claims for coherent risk measures. J. Convex Analysis 26 (1) (2019).

Saul Jacka and Adriana Ocejo, On the regularity of American options with regime-switching uncertainty, Stoch. Proc. & Appl. 128 (3), 803-818 (2018). arXiv:1309.1404

Saul D. Jacka and Aleksandar Mijatović, On the policy improvement algorithm in continuous time, Stochastics, 89 (1), (2017)

Some older publications (which might still be interesting)

Aleksandar Mijatovic, Matija Vidmar and Saul Jacka, Markov chain approximations to scale functions of Levy processes, Stoch. Proc. & Appl., 125 (10), 3932-3957 (2015)

Saul Jacka and Amogh Deshpande, Game-theoretic approach to risk-sensitive benchmarked asset management, Risk and Decision Analysis, 5 (4), 163-176 (2015)

Aleksandar Mijatovic and Saul Jacka, Coupling and tracking of regime-switching martingales, EJP 20, Article 38, 1-39 (2015)

Saul Jacka, Aleksandar Mijatovic and Dejan Siraj, Mirror and synchronous couplings of Geometric Brownian motion, Stochastic Processes and their Applications, 124, 1055-1069 (2014)

Sigurd Assing, Saul Jacka, Adriana Ocejo, Monotonicity of the value function for a two-dimensional optimal stopping problem, Ann. Appl. Prob., 24, 1554-1584 (2014).

Aleksandar Mijatovic, Matija Vidmar and Saul Jacka, Markov chain approximations for transition densities of Levy processes, EJP 19, Article 7, 1-37 (2014)

Saul Jacka, A simple proof of Kramkov's result on uniform supermartingale decompositions. Stochastics 84, 599-602 (2012)

Saul Jacka, Peter Windridge and Jon Warren, Minimising the time to a decision. Ann. Appl. Prob. 21, 1795-1826 (2011)

Saul Jacka, Markov chains conditioned never to wait too long at the origin J. Appl. Probab. 46, 812-826 (2009)

Saul Jacka and Stephen Connor, Optimal co-adapted coupling for the symmetric random walk on the hypercube, J. Appl. Probab. 45, 703-713 (2008)

Saul Jacka and Marcus Sheehan, The noisy veto-voter model: a Recursive Distributional Equation on [0,1]. J. Appl. Probab. 45, 670-688 (2008)

Saul Jacka, Abdel Berkaoui and Jon Warren, No arbitrage and closure results for trading cones with transaction costs. Finance & Stochastics12, 583-600 (2008)

Saul Jacka and Jon Warren, Random orderings of the integers and card shuffling Stoch. Proc. and Appl. 117, 708-719 (2007)

Saul Jacka and Abdel Berkaoui, On the density of properly maximal claims in financial markets with transaction costs. Ann. Appl. Prob. 17 (2), 716-740 (2007)

Saul Jacka, Zorana Lazic and Jon Warren, 'Conditioning an additive functional of a Markov chain to stay non-negative I: survival for a long time'. Adv. Appl. Prob . 37 (4), 1015-1034 (2005)

Saul Jacka, Zorana Lazic and Jon Warren, 'Conditioning an additive functional of a Markov chain to stay non-negative II: hitting a high level'. Adv. Appl. Prob. 37 (4), 1035-1055 (2005)

K Hamza, S D Jacka & F C Klebaner,'The EMM conditions in a general model for interest rates'. Adv. Appl. Prob . 37 (2), 415-434 (2005)

S D Jacka & R Tribe, 'Comparisons for measure valued processes with interactions'. Ann. Probab . 31, 1679-1712 (2003)

S D Jacka, 'Avoiding the origin: a finite-fuel stochastic control problem'. Ann. Appl. Prob . 12, 1378-1389 (2002)

S D Jacka & J Warren 'Examples of convergence and non-convergence of Markov chains conditioned not to die'. Elec. J. Prob . 7 No. 1 (2002)

S D Jacka & J C Croft, 'The Hausdorff dimension of some snowflake-like recursive constructions'. Fractals 10, 199-208 (2002)

S D Jacka and G O Roberts 'On strong forms of weak convergence' Stoch. Proc. & Appl. 67, 41-53 (1997)

S D Jacka 'A martingale representation result and an application to incomplete financial markets'. Math. Finance 2, 23-34 (1992)

S D Jacka 'Optimal stopping and the American put'. Math. Finance 1(2), 1-14 (1991)

S D Jacka 'A note on the good lambda inequalities'. Sem. de Prob. XXIII 57-65, LNM 1372, Springer (1989)

Some lecture notes

The art of stochastic control

Optimal stopping and control-applications

Some talks

Regulation, Risk and (defined benefit) Pensions (a talk for the Royal Statistical Society and the Isaac Newton Institute Gateway)

Monetary Risk and Prudence in Pension Fund Valuation (a talk given at a Royal Society Workshop)

Optimal Stopping and Technical Analysis (a talk given at the Centre for Mathematical Research in Economics and Finance, Manchester)

Coupling and Control (a talk in celebration of Wilfrid Kendall)

Optimal Stopping, Smooth Pasting and the Dual Problem (a talk at Imperial College)

Multicurrency reserving for coherent risk measures ( a talk given at the 2nd Byrne Workshop at Ann Arbor)

Information-dependent control (a talk given at Liverpool)

Policy Improvement (a talk given at the Academy of Sciences and Humanities, Oslo)

Coupling and convergence (a talk for OxWaSP)

The problems of Statistics (this is the text of a talk I gave in 2003 to civil service statisticians).

Shuttling a diffusion (a talk at UBC Vancouver).

Optimal stopping with stochastic volatility (a talk at King's College London)

The veto-voter model ( a talk at Cambridge).

(Monetary) Risk Measures (an introductory talk at Warwick suitable for undergraduates)