Nikolai Dokuchaev
Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energy on the higher frequencies. These filters are sub-ideal meaning that a faster decay of the frequency response would lead to the loss of causality.
Nikolai Dokuchaev
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. In other words, a dimension reduction is achieved via a relaxed version of the Mutual Fund Theorem.
Peter Situmbeko Nalitolela, Nikolai Dokuchaev
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control can be formulated as matrix inequalities in frequency domain. Furthermore, we show that if the optimal control exists, then certain Lyapunov equations must have a solution. The optimal control is obtained by solving a deterministic linear-quadratic optimal control problem whose functional depends on the solution to the Lyapunov equations. Moreover, we show that under certain conditions, solvability of the Lyapunov equations is guaranteed. We also show that, if the frequency inequalities are strict, then the solution is unique up to equivalence.
Anna Knezevic, Nikolai Dokuchaev
We propose an algorithm which predicts each subsequent time step relative to the previous timestep of intractable short rate model (when adjusted for drift and overall distribution of previous percentile result) and show that the method achieves superior outcomes to the unbiased estimate both on the trained dataset and different validation data.