TITLE:
Portfolio Optimization in Jump Model under Inefficiencies in the Market
AUTHORS:
Dereje Bekele, Ananda Kube, Dennis C. Ikpe
KEYWORDS:
Information Asymmetry, Inefficiencies, Optimal Portfolio, Jump Model, Power Utilities
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.8 No.3,
August
9,
2018
ABSTRACT: 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.