Continuous Time Processes with Stable Increments

Variance Optimal Hedging for continuous time processes with independent increments and applications

For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market are performed.

Stable fixed-lag smoothing of continuous time processes

Attempts to realize optimal fixed-lag smoothers for conIf one turns to the earlier literature, one can find, as is well tinuous-time processes have encountered two major difficulties: the known, descriptions of fixed-lag smoothers (for stationary presence of delay lines in the smoother, and the instability of most problems only) in the work of Wiener [13]. The optimal smoothers. This paper cons...

On $L_1$-weak ergodicity of nonhomogeneous continuous-time Markov‎ ‎processes

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Representations of Gaussian processes with stationary increments

Nonstationary Continuous - Time Processes ∗

∗Preliminary Comments are welcome. Paper written for the Handbook of Financial Econometrics edited by Yacine Aı̈t-Sahalia and Lars Peter Hansen. We thank Darrell Duffie, Benoit Perron and Mark Watson for discussions and Seoyeon Lee for research assistance. Bandi acknowledges financial support from the IBM Corporation Faculty Research Fund at the University of Chicago. Phillips thanks fhe NSF for...