Modified Constant Elasticity of Variance Model and Application to Portfolio Optimization with Managerial Charges

Saheed K. Olarewaju

Abstract

In this research, the optimal control strategy (OCS) for a pension fund member (PFM) in defined contribution pension scheme (DCPS) with managerial charges and constant extra voluntary contribution (EVC) rate is studied when the price process of the risky asset is modeled by a stochastic volatility model known as the modified constant elasticity of variance (MCEV). We consider a portfolio for the PFM with a risk free asset and a risky asset modeled by the M-CEV model. Also, a stochastic differential equation involving the PFM’s mandatory monthly contributions and managerial charges is considered. Furthermore, an optimization problem is obtained and solved using Legendre transformation and dual theory together with change of variables method for the analytical solution of the OCS and the value function under exponential utility. Moreso, we used the MATLAB software to present some numerical simulations of the impact of some sensitive parameters on the OCS and were discussed extensively with observation that the OCS is a decreasing function of the risk free interest rate, instantaneous volatility, risk averse, initial fund size, elasticity parameter and modification factor but an increasing function of the managerial charges and time.

Source: semanticscholar

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