**
**### Publications

### Books

1.

*Computational Financial Mathematics using Mathematica : optimal trading in stocks and options*, hardcover (with CD-ROM), xii+481 pp.,

** **Birkhäuser, Boston, 2003 (2

^{nd} edition in preparation under contract with

**Springer**).

2. Risk Premium, Interest Rates, Equity, and Foreign Exchange (a tentative title), in preparation under contract with

**Springer**.

### Papers

3. (with A. Friedman) A free boundary problem associated with icing in a channel, Nonlinear Analysis T.M.A., 11, 501-526 (1987); MR: 88i:35181.

4. (with J. Yong) Optimal switching for systems governed by nonlinear evolution equations, Numer. Funct. Analysis & Optimiz., 9, 995-1030 (1987); MR: 88k:49033.

5. Injection of ideal fluid from a slot into a stream: two free boundaries, IMA J. Appl. Math. 41, 237-253 (1988); MR: 90a:76049.

6. Injection of ideal fluid from two slots into a stream, Math. Meth. Appl. Sci. 10, 585-594 (1988); MR: 89k:76012.

7. (with J. Yong) Optimal switching for partial differential equations I, J. Math. Analysis & Appl., 138, 418-438 (1989); MR: 90c:49054.

8. (with J. Yong) Optimal switching for partial differential equations II, *J. Math. Analysis & Appl*., 138, 439-460 (1989); MR: 90c:49054.

9. Optimal damping control and nonlinear parabolic systems, *Numer. Funct. Analysis & Optimiz*., 10, 573-591 (1989); MR: 90i:49005.

10. (with P. Korman and A. Leung) Monotone iterations for nonlinear obstacle

problem, *J. Austral. Math. Soc*. Ser. B, 31, 259-276 (1990); MR: 91e:35108.

11. Direct Study for some nonlinear elliptic control problems, *Mathematics of Nonlinear Science*, Melvyn S. Berger, Editor, AMS Contemporary Mathematics,

Vol. 108, 145-153 (1990); MR: 91f:49003.

12. (with S. Lenhart and V. Protopopescu) A two-sided game for competitive systems with non-local interactions, *Proceedings of the 29th IEEE Conference on Decision and Control*, Volume 2, 1030-1031 (1990).

13. (with A. Leung) Direct methods for some distributed games, *Differential and*

Integral Equations, 3, 1099-1111 (1990); MR: 92a:49011.

14. Optimal damping control and nonlinear elliptic systems, *SIAM J. Control & Optimiz*., Vol. 29, No. 3, 594-608 (1991); MR: 91m:49001.

15. (with S. Lenhart and V. Protopopescu) Variational approach for competitive

systems with obstacles, *Applied Mathematics & Comp*., Vol. 42, 65-83, (1991); MR: 92e:90139.

16. Computations for variational free boundary problem modeling injection of fluid from a slot into a stream, *Theoretical Aspects of Industrial Design*, V. Komkov and D.A. Field, Editors, SIAM, 105-115 (1992); MR: 93c:76082.

17. Nonsmooth Analysis and Shape Optimization in a Flow Problem, *Proceedings of*

the 31^{st} IEEE Conf. on Decision and Control, Volume 4, 3117-3118 (1992).

18. (with A. Leung) Optimal control for elliptic Volterra-Lotka type equations, *J. Math. Analysis & Appl*., Vol. 173, No. 2, 603-619 (1993); MR: 94c:35035.

19. (with V. Barbu) Controlling the moving boundary of the parabolic obstacle problem, *Appl. Math. & Optimiz*., Vol. 27, No. 3, 213-230, (1993); MR: 93k:93012.

20. (with V. Barbu) A variational approach to a free boundary problem arising in electrophotography, *Numer. Funct. Anal. & Optimiz*., Vol. 14, No. 1&2,1-14 (1993); MR: 94c:35173.

21. (with S. Lenhart and V. Protopopescu) A minimax problem for semilinear nonlocal competitive systems, *Appl. Math. & Optimiz*., Vol. 28, No. 2,113-132 (1993); MR: 94g:49018.

22. (with S. Lenhart and V. Protopopescu) A two-sided game for non-local competitive systems with control on source terms, *Variational and Free Boundary Problems*, A. Friedman and J. Spruck, Eds., Springer, New York,135-152 (1993); MR: 95k:90140.

23. (with F. He and A. Leung) Periodic optimal control for parabolic competitive Volterra-Lotka type systems, *J. Comp. Appl. Math*., 52, 199-217 (1994); MR: 96b:49008.

24. (with T. Svobodny) A variational approach to shape optimization for the Navier-Stokes equations, *Optimal Control of Differential Equations*, N. H. Pavel, Editor,

Marcel Dekker, New York, 281-292 (1994); MR: 95h:35180.

25. Nonsmooth analysis and free-boundary problems, *Boundary Control and*

Variation, J-P. Zolesio, Editor, Marcel Dekker, New York, 367-382 (1994);

MR: 95h:49042.

26. (with F. He and A. Leung) Periodic optimal control for parabolic Volterra-Lotka type equations, *Math. Meth. Appl. Sci*. 18, 127-146 (1995); MR: 95j:49005.

27. (with T. Svobodny) Free boundary problems for potential and Stokes equations via nonsmooth analysis, *SIAM** J. Math. Anal*., 26, 633-658 (1995).

28. Nonsmooth Analysis and Free Boundary Problems for Potential Flow, *Flow Control*, M. Gunzburger, Editor, Springer-Verlag, New York, 275-295 (1995); MR: 96b:49003.

29. (with D. Geltner and T. Riddiough) Insights on the effect of land use choice: The perpetual option on the best of two underlying assets, *J. Urban Economics*, 39, 20-50 (1996).

30. Perturbation formula for regular free boundaries in periodic-parabolic equations and minimization of extinction, *Proceedings of the 36th IEEE Conf. on Decision and Control* (1997).

31. Perturbation formula for regular free boundaries in elliptic and parabolic obstacle problems, *SIAM J. Control & Optimiz*., Vol. 35, No. 6 (1997).

32. Modeling and minimization of extinction in Volterra-Lotka type equations with free boundaries, *J. Differential Equations*, 134, 320-342 (1997).

33. Multivariate constrained portfolio rules: derivation of Monge-Ampere equations, *Control of Distributed Parameter and Stochastic Systems*, S. Chen, X. Li, J. Yong, and X.Y. Zhou Editors, Kluwer Academic Publishers, (1999).

34. Implied volatility for American options via optimal control and fast numerical solutions of** **obstacle problems, *Differential Equations and Control Theory*, Aizicovici and Pavel, Editors, Marcel Dekker, 277-294 (2001).

35. Optimal momentum hedging via Monge–Ampère PDEs and a new paradigm for pricing options, *SIAM J. Control & Optimization*, 43 (2004) 1151-1173.

36. Optimal portfolio series formula under dynamic appreciation rate uncertainty, *Journal for Computational Finance*, 8 (2) (2005).

37. Risk premium and fair option prices under stochastic volatility: the HARA solution, *C. R. Acad. Sci. Paris Ser. I* 340 (2005) 551-556.

42. Stochastic control approach to derivative pricing and hedging in incomplete markets modeled by general Itô SDE systems: an overview and an application in FX derivatives, *Proceedings of the American Control Conference*, IEEE Omnipress, (2007) 1115-1119.

43. Equity valuation: market-share-dynamics effect on the value of multiple product lines, accepted, to appear in Risk Management in Financial Institutions, Volume 2, No 3, available at SSRN:

http://ssrn.com/abstract=1067627

**Preprints:**

46. Risk premium for Vasicek model: humped yield curve modeling, September 2007.

**Lecture Notes:**

1. Equities, Derivatives, Risk Premium and Portfolio Optimization, GARP, November and December 2006, New York and London.

2. Stochastic Volatility and Risk Premium, GARP, May and October 2005, New York and London.

## Talks

1. Optimal switching for infinite dimensional systems, Combined Midwest-Southeast Differential Equations Conference, Vanderbilt University, Nashville, TN, October 23-24, 1987.

2. On some free boundary problems, colloquium, Department of Mathematics, Wright State University, Dayton, OH, November 6, 1987.

3. On some free boundary problems, Science Alliance Seminar, Department of Mathematics, University of Tennessee, Knoxville, TN, January 21, 1988.

4. Implicit damping control and nonlinear parabolic systems, PDE Seminar, Department of Mathematics, Iowa State University, Ames, IA, October 27, 1988.

5. Optimal damping control and nonlinear elliptic systems, 17th Midwest Differential Equations Conference -- Systems, Control and Differential Equations --, Iowa State University, Ames, IA, October 28 and 29, 1988.

6. Implicit damping control and nonlinear elliptic systems, 8th Annual Southeastern-Atlantic Regional Conference on Differential Equations, The University of Georgia, November 4 and 5, 1988.

7. Direct study for some nonlinear elliptic and parabolic control problems, AMS Special Session on Mathematics of Nonlinear Science, 95th Annual Meeting of the AMS, Phoenix, AZ, January 11-14, 1989.

8. Direct methods for nonlinear problems in optimal control of distributed systems, SIAM Conference on Control in the 90''s: Achievements, Opportunities, and Challenges, Cathedral Hill Hotel, San Francisco, CA, May 17-19, 1989.

9. Optimal control for elliptic Volterra-Lotka equations, Invited 1 hour talk, Conference on Control and Partial Differential Equations, University of Kentucky, Lexington, KY October 20, 1989.

10. Optimal control for elliptic Volterra-Lotka type equations, Colloquium, Department of Mathematics, University of New Orleans, New Orleans, LA 70148, November 17, 1989.

11. Analysis and computations in some nonlinear distributed control problems, AMS Special Session on Control of Infinite Dimensional Systems, 96th Annual Meeting of the AMS, Louisville, KY, January 17-20, 1990.

12. Controlling the moving boundary of the parabolic obstacle problem, 19^{th} Annual Southeastern-Atlantic Regional Conference on Differential Equations, Virginia Polytechnic Institute and State University, Blacksburg, VA, November 16-17, 1990.

13. A two-sided game for competitive systems with non-local interactions, 29^{th} IEEE Conference on Decision and Control, December 5-7, 1990, The Hilton Hawaiian Village, Honolulu, HI.

14. Distributed games and alternating monotone iterations, colloquium, Department of Mathematics, Wright State University, Dayton, OH, January 25,1991.

15. A variational approach to a free boundary problem arising in electrophotography, IMA Workshop: Variational Problems, April 15-19, 1991, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN 55455.

16. A minimax problem for a competitive system with nonlocal interactions, Second International Conference on Industrial and Applied Mathematics (ICIAM 91), July 8-12, 1991, Washington, D.C.

17. On some nonsmooth PDE optimization problems, Invited 45 min. lecture, 3^{rd} UK-UT Conference on Control and PDE''s, University of Kentucky, Lexington, KY, October 10, 1991.

18. Nonsmooth Analysis and Shape Optimization for Partial Differential Equations, SIAM Conference on Control and its Applications, September17-19, 1992, Minneapolis, Minnesota.

19. Nonsmooth Analysis and Shape Optimization for a Flow Problem, AMS Special Session on Control Theory and Partial Differential Equations, AMS Meeting, Dayton, Ohio, October, 1992.

20. Nonsmooth Analysis and Shape Optimization in Flow Problems, IMA Period of Concentration: Flow Control, University of Minnesota, Minneapolis, MN 55455, November 16-20, 1992.

21. Nonsmooth Analysis and Shape Optimization for Navier-Stokes Equations, IMA

Workshop on Nonsmooth Analysis and Geometric Methods in Control Theory, University of Minnesota, Minneapolis, MN 55455, February 8 - 17, 1993.

22. Nonsmooth Analysis and Shape Optimization for Navier-Stokes Equations, International Conference on Optimal Control of Differential Equations and Variational Inequalities, Athens, Ohio, March 25-27, 1993.

23. Nonsmooth Analysis and Shape Optimization for Navier-Stokes equations, AMS Special Session on Control and Applications, AMS Meeting in Knoxville, April 26-27, 1993.

24. On some Free Boundary Value Problems and Optimization, Department of Mathematics, University of Cantabria, Santander, Spain, October 7, 1993.

25. Free Boundary Problems and Optimization, Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061, October 26, 1993.

26. Optimal Control of Free Boundaries, Conference on Control of Partial Differential Equations, International Federation of Information Processes, Laredo, Spain, September 5-9, 1994.

27. Analysis and Optimization in Free Boundary Problems (Lecture Series), Departimento di Matematica, Universita degli Studi di Roma Tor Vergata, Roma, Italy, June 2 - July 2, 1995.

28. Higher Regularity via Monotone Operators for Parabolic Obstacle Problems, CIRM Conference on "Nonlinear Parabolic Problems," Levico Terme (Trento), Italy, June 11-16, 1995.

29. Optimal Control of Free Boundaries, Minisymposium on Domain Optimization, International Congress on Industrial and Applied Mathematics, Hamburg, Germany, July 3 - 7, 1995.

30. Lewy-Stampacchia Equations and Optimal Control of Free Boundaries, Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, November 3, 1995.

31. Modeling and Optimal Control of Extinction in Volterra-Lotka Type Equations with Free Boundaries, Dipartimento di Matematica, Universita degli Studi di Roma Tor Vergata, Roma, Italy, December 4, 1995.

32. On some Free Boundary Problems: Analysis, Optimal Control and Computations, Laboratory of Scientific Computing, University of Jyvaskyla, Finland, June11, 1996.

33. Modeling and Optimal Control of Extinction in Volterra-Lotka Type Equations with Free Boundaries, ECMI 96, DK-2800 Lyngby, Denmark, June 25-29, 1996.

34. Optimal Control in Volterra-Lotka Equations with Free Boundaries, Special Session on Nonlinear Systems, World Congress of Nonlinear Analysts, Athens, Greece, July 10-1, 1996.

35. Optimal control of free boundary for Volterra-Lotka type equations, CIRM Conference on "Viability and Control - II," Levico Terme (Trento), Italy, June 2-7, 1997. Presented also at:

36. Minisymposium on Optimal Control and Identification, Laboratory of Scientific Computing, University of Jyvaskyla, Finland, August 15, 1996.

37. Monge–Ampère type equations in financial mathematics, Colloquium, Department of Mathematics, Loyola University, Chicago, Illinois, November 14, 1997.

38. Optimal diversification under constraints: Monge–Ampère equations and computations, Symposium on Stochastic Control and Nonlinear Filtering, University of Southern California, Los Angeles, California, December 13-15, 1997.

39. Parabolic equations of Monge–Ampère type in finance: derivation and computations, International Conference on Nonlinear Partial Differential Equations and Applications, Northwestern University, Evanston, Illinois, March 21-24, 1998.

40. Optimal diversification under budget and no-short-selling constraints, Worldwide Mathematica Conference, Hotel Inter-Continental Chicago, Illinois, June 18-21, 1998.

41. Optimal portfolio diversification under budget and no-short-selling constraints, Conference on Control of Distributed Parameter and Stochastic Systems, Hangzhou, China, June 19-22, 1998.

42. Optimal diversification rules under budget and no-short selling constraints via numerical solutions of Monge–Ampère equations, Conference on Partially Observed Control with Financial Models of Incomplete Markets, in Honor of Professor Raymond W. Rishel, University of Kentucky, Lexington, Kentucky, October 2-3, 1998. Also presented at:

43. Workshop on Financial Models, October 22-23, 1998, Northwestern University, Evanston, Illinois.

44. Department of Mathematics, Fudan University, Shanghai, China, Colloquium, November 11, 1998.

45. Financial Mathematics Seminar, University of Chicago, Chicago, Illinois, December 4, 1998.

46. Stocks, options, pde''s and *Mathematica*, Department of Mathematics, Wright State University, Dayton, OH, Colloquium, February 12, 1999.

47. Implied volatility for European options via optimal control of pde''s, International Workshop on Diff. Equations ond Optimization Problems, Ohio University, Athens, Ohio, May 12 - 14, 2000.

48. Implied volatility for American options via optimal control of obstacle problems, Optimale Steurung komplexer dynamischer strukturen, Matematisches Forschunsinstitut Oberwolfach, Oberwolfach, Germany, June 4 - 10, 2000.

49. Optimal portfolios of stocks and options via numerical solutions of Monge–Ampère type pde''s, International Conference on Monte Carlo and Probabilistic Methods for PDE''s, Monte Carlo, Monaco, July 3 - 5, 2000.

50. Optimal Options via Numerical Solutions of Monge–Ampère PDEs, Quantitative Risk Management in Finance, Carnegie Mellon University, Pittsburgh, PA 15213-3890, July 31 - August 5, 2000.

51. Optimal portfolios of stocks and options via symbolic and numerical solutions of Monge–Ampère type pde''s: Optimal Hedging Rules, Conference on Mathematical Finance, University of Konstanz, Konstanz, Germany, October 5 - 7, 2000.

52. Fast numerical solutions and optimal control of obstacle problems in finance, PDE Seminar, Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, September 18, 2001.

53. Numerical hypoelliptic obstacle problems and optimal momentum trading, Probability Seminar, Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, January 14 2002.

54. On some Monge–Ampère and hypoelliptic equations in finance, *Colloquium*, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, November 7, 2002.

55. Computational Finance Seminar, Purdue University, West Lafayette, Indiana 47907, February 28, 2003.

56. AMS Special Session on Stochastic Analysis with Applications, April 4-6, 2003, Bloomington, Indiana.

57. AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance, June 22-26, 2003, Snowbird, Utah.

58. Mathematical aspects of financial portfolio optimization, Colloquium, Department of Mathematics, University of Dayton, January 15th, 2004.

59. Options Pricing, Portfolio Hedging, and Data Analysis, Part 1, 2, 3, and 4, IMA Short Course: Tools for Modeling and Data Analysis in Finance/Asset Pricing, March 29-April 2, 2004, Institute for Mathematics and Its Applications (IMA), University of Minnesota, Minneapolis, MN 55455.

60. Pricing options under stochastic volatility: complete solution, IMA Workshop 8: Model Implementation, Algorithms and Software Issues, University of Minnesota, May 3-7, 2004.

61. Optimal portfolio series formula under dynamic appreciation rate uncertainty, IMA, University of Minnesota, May 19, 2004.

62. Pricing options under stochastic volatility: the complete solution, Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations, Juan-les-Pins, France, June 7-10, 2004.

63. Risk premium and fair option prices under stochastic volatility, GARP’s 6th Annual Risk Management Convention & Exhibition, February 1-2, 2005, New York City.

64. PDE Methods in Financial Modeling, 25th Annual SEARCDE in Dayton, Ohio, October 7-8, 2005 (Invited Plenary Address).

65. Pricing and Hedging in Multidimensional Incomplete Markets under Stochastic Interest Rates, Department of Mathematics and Statistics, Wright State University, Dayton, OH, May 19, 2006.

66. Pricing and Hedging in Multidimensional Incomplete Markets under Stochastic Interest Rates, Department of Mathematics, Ohio University, Athens, OH, June 2, 2006.

67. Higher dimensional fair option pricing and hedging under HARA and CARA utilities, 4^{th} World Congress of Bachelier Finance Society, Tokyo, Japan, August 17-20, 2006.

68. The dividend puzzle unpuzzled, International Conference on Mathematical Finance and Related Topics, Kanazawa, Japan, August 21-23, 2006.

69. Derivative pricing and partial hedging under multi-dimensional risks in incomplete markets: theory and applications, Department of Mathematics, Tongji University, Shanghai, China, August 25, 2006.

70. Neutral derivative pricing and hedging under multi-dimensional risks in incomplete markets: theory and applications, AMS Special Session on Financial and Actuarial Mathematics, organized by Stojanovic and Zhong, Cincinnati OH, October 21-22, 2006.

71. Risk Premium, pricing, and hedging of financial contracts: the case of agricultural (seasonal) commodity futures, Faculty of Agriculture, University of Belgrade, Serbia, December 6, 2006.

72. Stochastic Control Approach to Derivative Pricing and Hedging in Incomplete Markets Modeled by General Ito SDE Systems: An Overview and an Application in FX Derivatives, 2007 American Control Conference, July 11-13, 2007, Marriott Marquis Hotel at Times Square, New York City, USA.

73. Financial Engineering of Leveraged Buyouts in Incomplete Markets,

Quant Congress USA 2007, July 11-13, 2007, Marriot Financial Centre, New York City, USA.

79. Foreign exchange rates and foreign exchange derivatives: an optimal portfolio based theory and applications in stochastic volatility, WCNA-2008, Orlando, Florida, July 2 – July 9, 2008.

80. Quantitative equity: Dividend policy, risk premium, and market share dynamics, WCNA-2008, Orlando, Florida, July 2 – July 9, 2008.

## Special Session Organized

**AMS Special Session on Financial and Actuarial Mathematics, organized by Stojanovic and Zhong, Cincinnati OH, October 21-22, 2006.**