Stochastic modelling of non-stationary financial assets

Non-Stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run avera...

Non - Stationary Bayesian Modelling and

Inventory routing with non-stationary stochastic demands

We solve a rich logistical problem inspired from practice, in which a heterogeneous xed eet of vehicles is used for collecting recyclable waste from large containers over a nite planning horizon. Each container is equipped with a sensor, which communicates its level at the start of the day. Given a history of observations, a forecasting model is used to estimate the point demand forecasts as we...

Prediction for Non-Stationary Stochastic Processes – II

A method is presented for extrapolation of time-series which contain time-varying frequency components. The time-series is complex-demodulated at a set of frequencies. The resulting time-frequency time-series are assumed to be time-dependent such that the amplitude and phase change relatively slowly with time. This change is taken into account in the extrapolation. This model of a non-stationar...

Treatment of Income: Analogy Between Non-financial and Financial Assets, December 23, 2000