I’m going to study a continuous time stochastic model of optimal consumption plan.

An agent invests his capital W₀ in some financial instrument. The instantaneous rate of return r(t) of this instrument is given by stochastic fractional differential equation. During persistence of the investment our rentier consumes part of his wealth. Therefore the dynamic of wealth process W(t) is described by the following equation   

W’(t) = W(t)r(t) – c(t), 

where c(t) is a consumption rate process. The point is to choose optimal consumption strategy with respect to power utility function u(x) = x^a,  0<a<1.

 I’ll present in my talk the properties of the solution of the stochastic control problem mentioned above.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/17836 must be provided.

1. Modelling of Short Term Interest Rate Based on Fractional Relaxation Equation
2. The Asymptotic Dependence of Elliptic Random Variables