Portfolio Management for a Random Field of Bond Returns

A new method of bond portfolio optimization is described. The method is based on stochastic string models of bond returns. It is shown how to approximate the bond return correlation function with Padé approximations and how to compute the optimal portfolio allocation using Wiener-Hopf factorization. The technique is illustrated with an example of the Treasury bond portfolio.bond portfolio management, stochastic string, Toeplitz operators, Padé approximations, Wiener-Hopf factorization.

Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.Lévy processes; barrier options;regime switching models; Wiener-Hopf factorization; Laplace transform; numerical methods; numerical transform inversion

Factorization of Laurent series over commutative rings

We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the algebraic nature of this factorization.Comment: 8 page

A note on Wiener-Hopf factorization for Markov Additive processes

We prove the Wiener-Hopf factorization for Markov Additive processes. We derive also Spitzer-Rogozin theorem for this class of processes which serves for obtaining Kendall's formula and Fristedt representation of the cumulant matrix of the ladder epoch process. Finally, we also obtain the so-called ballot theorem

The relationship between a strip Wiener-Hopf problem and a line Riemann-Hilbert problem

In this paper, the Wiener–Hopf factorization problem is presented in a unified framework with the Riemann–Hilbert factorization. This allows to establish the exact relationship between the two types of factorization. In particular, in the Wiener–Hopf problem one assumes more regularity than for the Riemann–Hilbert problem. It is shown that Wiener–Hopf factorization can be obtained using Riemann– Hilbert factorization on certain lines.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis.This is the final published version. It was first published by OUP at http://dx.doi.org/10.1093/imamat/hxv00