Author(s)

Dereje Bekele^1*, Ananda Kube², Dennis C. Ikpe³

¹Pan African University Institute for Basic Sciences, Technology and Innovation (PAUISTI), Juja, Kenya.
²Department of Statistics and Actuarial Sciences, Kenyatta University, Nairobi, Kenya.
³Department of Mathematical Sciences, University of South Africa, Florida, South Africa.

This paper evaluates the use of modeling approach that depends on Levy jump model to predict investors wealth under inefficiencies in the market, in terms of mispricing and asymmetric information where the traded stock or risky asset price is considered to be as a function of a Levy jump process (i.e. the driving Levy process has Brownian component) by specifying the asset price process in the large filtration of informed investor. Then we obtain its dynamics for uninformed investor using the Hitsuda representation of Gaussian processes assuming there are two distinct classes of rational investors. In this setting assuming power utility functions, the optimal portfolios, maximum expected power utilities and asymptotic utilities for investors from the terminal wealth are derived by the methods of optimization and stochastic calculus.

Information Asymmetry, Inefficiencies, Optimal Portfolio, Jump Model, Power Utilities

Bekele, D. , Kube, A. and Ikpe, D. (2018) Portfolio Optimization in Jump Model under Inefficiencies in the Market. Journal of Mathematical Finance, 8, 562-575. doi: 10.4236/jmf.2018.83036.