Methods in Risk Management Programme Director
Chair of Examiners Sub-board (QMRM)
dependent options. Quantile,
Parisian and Asian options. Lévy
Doubly stochastic point processes.
Dynamic contagion models.
Applications in insurance.
Ruin theory. Lévy
as appiled to financial and
insurance mathematics. Exact
Tests of association.
I am usually
looking for prospective PhD students that show
initiative. Any ideas combining two or
more of these areas are especially welcome or
even ideas outside them. You are advised to have
a look at some of my papers before contacting
A Two-Phase Dynamic Contagion Model
(with Z.Chen, V.Kuan, J.W.Lim,
Y.Qu, B.Surya and H.Zhao)
An edited version will appear in Results in
In this paper, we propose a continuous-time
stochastic intensity model, namely, two-phase
dynamic contagion process (2P-DCP), for modelling
the epidemic contagion of COVID-19 and investigating
the lockdown effect based on the dynamic contagion
model introduced by Dassios and Zhao (2011). It
allows randomness to the infectivity of individuals
rather than a constant reproduction number as
assumed by standard models. Key epidemiological
quantities, such as the distribution of final
epidemic size and expected epidemic duration, are
derived and estimated based on real data for various
regions and countries. The associated time lag of
the effect of intervention in each country or region
is estimated. Our results are consistent with the
incubation time of COVID-19 found by recent medical
study. We demonstrate that our model could
potentially be a valuable tool in the modeling of
COVID-19. More importantly, the proposed model of
2P-DCP could also be used as an important tool in
epidemiological modelling as this type of contagion
models with very simple structures is adequate to
describe the evolution of regional epidemic and
Finite and Infinite
doi: 10.1080/01605682.2019.1657368 (with Y.Qu
Brownian Motion with
Drift on Rays and
its Application in
Banking, 2020, Risks, 8(4), 127 (with J.
Simulation of Lévy-driven
Point Processes, 2019, Advances of
Applied Probability, 51(4), 927-966 (with Y.Qu and
Simulation of Generalised Vervaat
of Applied Probability,
56(1), 57-75, (with J.W.Lim
A Variation of
the Azema Maringale and Drawdown
1116-1130 (with J.W.Lim)
Generalised CIR Process with
Self-Exciting Jumps and its
Applications in Insurance and
103 (with J.Jang and H.Zhao)
for a Class of Tempered Stable and
Related Distributions, 2018,Transactions
on Modeling and Computer Simulation
(TOMACS), 28(3)(with Y.Qu and H.Zhao).
Moments of Renewal Shot-Noise
Processes and Applications, 2018,Scandinavian
Actuarial Journal, 8,
(with J. Jang and H.Zhao)
formula for the double barrier
Parisian stopping time, 2018,Journal
of Applied Probability,55(1), 282-301 (with J.W. Lim)
Simulation of Clustering Jumps with
CIR Intensity, 2017, Operations
Testing independence of
covariates and errors in
nonparametric regression, 2017,Scandinavian Journal of
Statistics, 45(3), 421-443, (with W. P.
Bergsma and S.S. Dhar)
An efficient algorithm for
simulating the drawdown stopping
time and the running maximum of a
Brownian motion, 2017,Methodology
and Computing in Applied
Probability, 19(1), 1-16,
A Generalised Contagion
Process with An Application to
International Journal of
Theoretical and Applied Finance, 20(1),
1-33, (with H. Zhao).
The joint distribution of
Parisian and hitting times of Brownian motion with
application to Parisian option
pricing, 2016, Finance and
773-804 (with Y. Zhang).
A study of the power
and robustness of a new test for
independence against contiguous
alternatives, 2016, Electronic
Journal of Statistics,10
(1). pp. 330-351 (with W. P.
Bergsma and S.S. Dhar).
An analytical solution
for the two-sided Parisian stopping
time, its asymptotics, and the
pricing of Parisian options, 2015, Mathematical
A risk model with
renewal shot-noise Cox process,
2015, Insurance: Mathematics
& Economics, 65,
55–65 (with J. Jang and H. Zhao).
A consistent test of
independence based on a sign
covariance related to Kendall's tau,2014,
Bernoulli , 20(2),
1006-1028 (with W. P. Bergsma).
A Markov chain model for
contagion , Risks 2014, 2,
(with H. Zhao).
Parisian option pricing: A
recursive solution for the density
of the Parisian stopping time, 2013,
SIAM J. Financial Mathematics,
4(1), 599-615 (with J. W.
crossing probabilities for the
Brownian motion, 2013, Journal
of Applied Probability, 50(2),
419-429 (with X. Che).
Exact simulation of Hawkes
process with exponential decaying
Intensity, 2013, Electronic
Communications in Probability
(with H. Zhao).
A risk model with delayed
claims, 2013, Journal of Applied
686-702 (with H. Zhao).
A bivariate shot noise
process for insurance , 2013, Insurance
Mathematics and Economics, 53(3),
Ruin by Dynamic Contagion
Insurance Mathematics and
Double barrier Parisian
options , 2011, Journal of
Applied Probability , 48(1),
1-20 (with S. Wu).
A dynamic contagion
process, 2011, Advances in
Applied Probability , 43(3),
814-846 (with H. Zhao).
A double shot noise process
and its application in insurance ,
2011, Journal of Mathematics and
System Science. (with J.
Perturbed Brownian motion
and its application to Parisian
option pricing, 2010, Finance
and Stochastics , 14,
473-494 (with S. Wu).
On barrier strategy
dividends with Parisian
implementation delay for classical
surplus processes, 2009, Insurance
Mathematics and Economics, 45,
195-202 (with S. Wu).
The distribution of the
interval between events of a Cox
process with shot noise intensity, Journal
of Applied Mathematics and
Stochastic Analysis, 2008,Article
ID 367170 (with J. Jang)
Bonds and options valuation
using a conditioning factor approach
, Management Dynamics, 2007,
7(2), 25-69 (with S. Basu).
root process and Asian options, Quantitative
Finance, 2006, 6(4),
337-347. (with J. Nagaradjasarma).
quantiles of the Brownian motion and
their hitting times, 2005, Bernoulli,
Kalman-Bucy filtering for
linear system driven by the Cox
process with shot noise intensity
and its application to the pricing
of reinsurance contracts, 2005, Journal
of Applied Probability, 42(1),
93-107 (with J. Jang).
Pricing of catastrophe
reinsurance & derivatives using
the Cox process with shot noise
intensity, 2003, Finance and
Stochastics , 7(1),
73-95(with J. Jang).
Cox process with log-normal
density, 2002, Insurance,
Mathematics and Economics, 31(2),
297-302 (with S. Basu).
Beta-Geometric in comparative
fecundability studies, 1998, Biometrics,
54(1), 140-146 (with R.
Sample quantiles of
additive renewal reward processes,
1996, Journal of Applied
Sample quantiles of
stochastic processes with stationary
and independent increments and of
sums of exchangeable random
variables, 1996, Annals of
Applied Probability, 6(3),
The distribution of the
quantiles of a Brownian motion with
drift and the pricing of related
path dependent options, 1995, Annals
of Applied Probability, 5(2),
Martingales and insurance
risk, 1989, Communications in
Statistics, Stochastic Models,
5(2), 181-217, (with P.
links to a few of my papers as well as some