· Office: N517 Ross Bldg.

· Phone: (416) 736-5250 ext.66091

· Fax: (416) 736-5757

·
Email:
hku@mathstat.yorku.ca

**Research Interests:**

**Mathematical Finance and Stochastic Analysis;**

My research concerns developing the
mathematical models and theory for financial applications, and applying the
results to financial markets.
This is an interesting research area with fascinating and challenging research
problems, and
uses a wide variety of knowledge and techniques from probability, stochastic
processes, functional analysis, numerical analysis, Monte Carlo, stochastic
control and partial differential equations. The topics include development of derivatives valuation models,
analysis of financial market, portfolio management and risk evaluation, and
stochastic modeling. Recently,
research projects on Liquidity risk, Price impact, Optimal execution
strategies, Derivatives pricing, Filtering, Information asymmetry, High
frequency trading and Machine learning have been completed or are ongoing.

**Publications:**

“Option
Pricing for a Large Trader under Price Impact and Liquidity Costs” with H.
Zhang, *Journal of Mathematical Analysis
and Applications* 459*,* pp.32-52
(2018, .pdf)

“Portfolio
Optimization for a Large Investor under Partial Information and Price Impact”
with Z. Eksi, *Math Meth Oper Res* 86*,* pp.601-623 (2018, .pdf)

“Option
Valuation with Liquidity Risk and Jumps” with H. Zhang, *Appl. Econ. Lett. *25, pp.381-387 (2018, .pdf)

“Closed-form
Solutions for Options with Random Initiation under Asset Price Monitoring” with D. Jun, *Finance Research Letters* 20*, *pp.68-74
(2017, .pdf)

“Option
Replication in Discrete Time with the Cost of Illiquidity” with Y. Sorokin, *Communications in Mathematical Sciences*
14, No.7, pp. 1947-1962 (2016, .pdf)

“Local Volatility Model with Stochastic Interest Rates” with B. Hu, P. Wu, H. Zhu, Under Revision (2016)

“Static Hedging of Chained-Type Barrier
Options” with D. Jun, *North American
Journal of Economics and Finance* 33, pp.317-327 (2015, .pdf)

“Analytic Solutions for American Barrier
Options with Two Barriers” with D. Jun, *Journal of Mathematical Analysis and Applications* 422, pp. 408-422
(2015, .pdf)

“Valuation
of Claims with Price Impact Functions and Liquidity Costs” with H. Zhang, The
Isaac Newton Institute, University of

“A Study on Exotic Derivatives with Barriers: An Introduction to Chained Options” with D. Jun (2014)

“Pricing
Chained Options with Curved Barriers” with D. Jun, *Mathematical Finance* 23, No. 4, pp.763-776 (2013, .pdf)

“Digital
Barrier Option Contract with Exponential Random Time” with D. Jun, *IMA Journal of Applied Mathematics* 78,
pp.1147-1155 (2013, .pdf)

“Valuation
of American Partial Barrier Options” with D. Jun, *Review of Derivatives Research* 16, No.2, pp 167-191 (2013, .pdf)

“Discrete
Time Hedging with Liquidity Risk” with K. Lee and H. Zhu, *Finance Research Letters* 9, pp.135-143 (2012, .pdf)

“Financial Contracts Linked with Barrier Options of Exponential Monitoring” with D. Jun (2012)

“Cross
a Barrier to Reach Barrier Options” with D. Jun*, Journal of Mathematical Analysis and Applications* 389, pp.968-978
(2012, .pdf)

“Randomized
Stopping Times and Coherent Multiperiod Risk Measures”, *Stochastics* 83, pp.223-231 (2010, .pdf)

“Coherent
Multiperiod Risk Adjusted Values and Bellman's Principles” with P. Artzner, F.
Delbaen, J.M. Eber, and D. Heath, *Annals
of Operations Research* 152, pp.5-22 (2007, .pdf)

“Consistency
among Trading Desks” with D. Heath, *Finance
and Stochastics* 10, pp.331-340 (2006, .pdf)

“Liquidity
Risk with Coherent Risk Measures” *Applied
Mathematical Finance* 13, pp.131-141 (2006, .pdf)

“Measurement
of Financial Risk”, *Proceedings of the
UKC (US-Korea Conference) on Science and Technology*,

“Pareto
Equilibria with Coherent Measures of Risk” with D. Heath, *Mathematical Finance* 14, pp.163-172 (2004, .pdf)

“Valuation
and Hedging of Options with General Payoff under Transaction Costs” with H.I.
Choi and D. Heath, *J. Korean Math Soc.*
41, pp.513-533 (2004, .pdf)

“Multiperiod Risk and Coherent Multiperiod Risk Measurement” with P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, ETH-Zurich (2003, .pdf)

“Coherent Multiperiod Risk Measurement” with P. Artzner, F. Delbaen, J.M. Eber, and D. Heath, ETH-Zurich (2002, .pdf)

“The Consistency of Two Markets” with D. Heath,

“Valuation
and Hedging of Options in the Markets with Daily Price Limit” with J. Ban and
H.I. Choi, *Applied Mathematical Finance*
7, pp.61–74 (2000, .pdf)

“Option Valuation and Hedging for the Stochastic Volatility Model: New Iterative PDE Method” with H.I. Choi, (1998, .pdf)

“Existence
of Solutions for p-Laplacian Type Equations” with J. Kim, *J. Korean Math Soc.* 33 (1996) pp.291–307

**PhD/PDF supervision:**

· Kaiyan Lin (PhD), in progress

· Richard Le (PhD), in progress

· Morgans Wang (PhD), in progress, cosupervision

· Bing Hu (PhD), in progress, cosupervision

· Hai Zhang (PhD), Completed in 2017, now a manager of Model Validation at
Scotiabank

· Yegor Sorokin (PhD), Completed in 2014, now a manager of Capital Markets
Risk Management at CIBC

· Doobae Jun (PDF), Completed in 2012, now an associate professor at

**FE (Financial
Engineering) Diploma program at ****:**

The Financial Engineering Diploma is a
collaborative program established in 1998 in cooperation with the Schulich School of Business.
The Graduate Diploma in Financial Engineering is a concurrent program offered
to MBA students in the Schulich School of Business and to MA students in the
Department of Mathematics and Statistics.

Students who obtain the Graduate Diploma in
Financial Engineering concurrently with an MA in Mathematics and Statistics get
the best from both worlds: rigorous training in Mathematics offered by the
Department of Mathematics and Statistics coupled with several specialized
courses in Mathematical Finance offered by the Schulich School of Business.
This unique combination opens doors to many exciting careers in the Financial
Industry all over the world.

**Teaching:**

(Winter
2016)

· **MATH
6910** Stochastic Calculus in
Finance

(Fall 2015)

· **MATH 1581** Business Mathematics I

· **MATH 1550** Mathematics with Management
Applications

(Winter 2014)

· **MATH
6910** Stochastic Calculus in
Finance

·** ****MATH 2581** Business Mathematics II

(Winter 2013)

· **MATH
4430 / 6602** Stochastic
Processes