|C. Douglas Howard, Associate Professor|
My current research falls into two broad areas of application of probability theory: spatially disordered systems, and computational finance.
Spatially disordered systems is a class of probabilistic models generally motivated by physical problems arising in condensed matter physics and materials science. Two types of systems that I study are called first-passage percolation (FPP) and stochastic Ising dynamics. FPP has applications in areas as seemingly diverse as properties of porous media (aquifers, membranes, etc.), the growth of cancerous tumors, the propagation of cracks through concrete, and the flow of electricity through networks. Ising models capture some of the fundamental features of magnetized materials.
My work in computational finance generally focuses on the application of probabilistic methods and arbitrage-free pricing theory in valuing financial instruments and quantifying risk. It is practical in nature, much of it motivated directly by industry applications.
Models of First-Passage Percolation, (C.D. Howard), Probability on Discrete Structures, (H. Kesten, Ed.), Springer-Verlag, 2004, 125 -
Geodesics and Spanning Trees for Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Annals of Probability, 29(2001), 577-623.
Lower Bounds for Point-to-Point Wandering Exponents in Euclidean First-Passage Percolation, (C.D. Howard), Journal of Applied Probability, 37(2000), 736-747.
Zero-Temperature Ising Spin Dynamics on the Homogeneous Tree of Degree Three, (C.D. Howard), Journal of Applied Probability, 37(2000), 736-747.
From Greedy Lattice Animals to Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Perplexing Problems in Probability: Papers in Honor of Harry Kesten, Birkhauser (M. Bramson and R. Durrett, Eds.), 1999.
Good Paths Don't Double Back, (C.D. Howard), The American Mathematical Monthly, 105(1998), 354-357.
Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Probability Theory and Related Fields, 108(1997), 153-170.
Distinguishing Certain Random Sceneries on Z via Random Walks, (C.D. Howard), Statistics and Probability Letters, 34(1997), 123-132.
Orthogonality of Measures Induced by Random Walks with Scenery, (C.D. Howard), Combinatorics, Probability, & Computing, 5(1996), 247-256.
Detecting Defects in Periodic Scenery by Random Walks on Z, (C.D. Howard), Random Structures and Alogrithms, 8(1996), 59-74.
Numerical Pitfalls of Latticed-Based Duration and Convexity Calculations, (C.D. Howard), Advances in Fixed-Income Valuation Modeling and Risk Management, Frank J. Fabozzi Associates, 1996, 327-336.
Valuing Path-Dependent Securities: Some Numerical Examples, (C.D. Howard), Advances in Fixed-Income Valuation Modeling and Risk Management, Frank J. Fabozzi Associates, 1996, 49-68. Also appears in: Investment Management for Insurers, (D.F. Babbel and F.J. Fabozzi, eds.) Frank J. Fabozzi Associates, 1999, 269-286.
Embedded Call Options and Refunding Efficiency, (C.D. Howard and A.J. Kalotay), Advances in Futures and Options Research, Vol. 3 (F.J. Fabozzi, ed.) JAI Press Inc, 1988, 97-117.
Long-Term Debt and Equity Markets and Instruments, (C.D. Howard and
A.J. Kalotay) Handbook of Financial Markets and Institutions, (E.I. Altman,
ed.) John Wiley & Sons, 1987, 5.1-5.37.