Santa Clara University

Research - Research Initiatives Search Form

Ofice of Research Initiatives

Research Initiatives

 
Main Menu and Search Form »

Daniel Ostrov

E-mail dostrov@scu.edu
School College of Arts and Sciences
Department Mathematics and Computer Science Department
Degrees
PHD, 1994, Brown University, Applied Mathematics
Research Interest Applied Mathematics: Specialize in Partial Differential Equations that arise in Finance, Economics, Engineering, Chemistry, and Physics. I have studied non-linear, first order hyperbolic partial differential equations called Conservation Laws and Hamilton-Jacobi equations. I have shown how to use these equations to study shape from shading, which reconstructs a 3-D surface by exploiting a 2-D picture (or radar image) of the surface, and chromatography, which is a chemical separation process. I have also looked at the effect on existence and uniqueness of a solution when the functions that comprise these equations have discontinuities. Recently, I have concentrated more on issues from Financial Mathematics. I have examined linear partial differential equations that describe how to price stock options, analyzed the effect of transaction costs on optimal investment strategies, and studied optimal investment strategies in the presence of taxes, in particular quantifying the effect of reaping tax losses wherever possible.
Publications, Performances, Exhibits or Papers Presented

1. Daniel N. Ostrov and Thomas G. Wong, "Optimal Asset Allocation for Passive Investing with Tax Benefits from Continuous Time Capital Loss Harvesting", in preparation

2. Jonathan Goodman and Daniel N. Ostrov, "An Option to Reduce Transaction Costs", submitted

3. Jonathan Goodman and Daniel N. Ostrov, "Balancing Small Transaction Costs with Loss of Optimal Allocation in Single and Multiple Stock Portfolios", submitted

4. Daniel Friedman and Daniel N. Ostrov, "Conspicuous Consumption Dynamics", Games and Economic Behavior, 61, 2008, no. 1, pp. 121-145

5. Daniel N. Ostrov, "Nonuniqueness for the Vanishing Viscosity Solution with Fixed Initial Condition in a Nonstrictly Hyperbolic System of Conservation Laws", Journal of Mathematical Analysis and Applications, 335, 2007, pp. 996-1012.


6. Daniel N. Ostrov, "An Example of Nonuniqueness for the Viscous Limit of a Non-strictly Hyperbolic System of Equations", Hyperbolic Problems, Theory, Numerics and Applications, Yokohama Publishers, 2006, pp. 213-218.


7. Daniel N. Ostrov, "Nonuniqueness in Systems of Hamilton-Jacobi equations", Optimal control, stabilization and nonsmooth analysis, pp. 49-59, Lecture Notes in Control and Inform. Sci., 301, Springer, Berlin, 2004.


8. Jonathan Goodman and Daniel N. Ostrov, "On the Early Exercise Boundary of the American Put Option", SIAM Journal of Applied Mathematics, 62, 2002, no. 5, pp. 1823-1835.


9. Daniel N. Ostrov, "Solutions of Hamilton-Jacobi Equations and Scalar Conservation Laws with Discontinuous Space-time Dependence", Journal of Di fferential Equations, 182, 2002, no. 1, pp. 51-77.


10. Joseph Kain and Daniel N. Ostrov, "Numerical Shape From Shading for Discontinuous Photographic Images", International Journal of Computer Vision, 44, 2001, no. 3, pp. 163-173.


11. Daniel N. Ostrov, "Solutions to scalar conservation laws where the  flux is discontinuous in space and time", Hyperbolic problems: theory, numerics, applications (Magdeburg, 2000), Internat. Ser. Numer. Math., 140, 141, Birkhuser, Basel, 2001, pp. 785-790.


12. Daniel N. Ostrov, "Extending Viscosity Solutions to Eikonal Equations with Discontinuous Spatial Dependence", Nonlinear Analysis, Vol. 42, no. 4, Aug. 2000, pp. 709-736.


13. Daniel N. Ostrov,"Viscosity Solutions and Convergence of Monotone Schemes for Synthetic Aperture Radar Shape-From-Shading Equations with Discontinuous Intensities", SIAM Journal of Applied Mathematics, Vol. 59, no. 6, 1999, pp. 2060-2085.


14. Daniel N. Ostrov, "Boundary Conditions and Fast Algorithms for Surface Reconstructions from Synthetic Aperture Radar Data", IEEE Transactions on Geoscience and Remote Sensing, Vol. 37, no. 1, 1999, pp. 335-346.


15. Daniel N. Ostrov, "Unique Solutions to Discontinuous Hamilton-Jacobi Equations in Shape-From-Shading", Proceedings from the Seventh International Conference in Zurich on Hyperbolic Problems: Theory, Numerics, Applications, International Series of Numerical Mathematics, Vol. 130, 1999, pp. 767-772.


16. Daniel N. Ostrov and Rudy Rucker, "Continuous Valued Cellular Automata for Nonlinear Wave Equations", Complex Systems, Vol. 10, 1996, pp. 91-119.


17. Daniel N. Ostrov, "Asymptotic Behavior of Two Interreacting Chemicals in a Chromatography Reactor", SIAM Journal of Mathematical Analysis, Vol. 27, No. 6, Nov.1996, pp. 1559-1596.


18. Daniel N. Ostrov, "Boundary Conditions for Chromatography Reactors in a State of Maximum Mixedness", Quarterly of Applied Mathematics, Vol. 55, No. 3, Sept. 1996, pp. 571-582.


19. Lewis Wedgewood, Daniel N. Ostrov, and Robert B. Bird, "A Finitely Extensible Bead-Spring Chain Model for Dilute Polymer Solutions", Journal of Non-Newtonian Fluid Mechanics, Vol. 40, 1991, pp.119-139.
Established 1851