The construction of optimal hedging portfolio strategies of an investor
AbstractWe consider the process of constructing an optimal hedging portfolio
strategies of an investor. This require the hedging out of risks associated with an investor’s portfolio process. In order to achieve this, there is the need for portfolio diversification, that is, investing into different number of investment firms. When the returns from a firm falls below expectation, the returns from other firms can be use to complement the loss. We categorised the investor’s portfolio into two folds: the initial investment and the capital gain. Our aim is to construct an hedged portfolio process
that can capture all the investor’s investment in i, i = 1, 2, …, N investment company at time t, using stochastic differential equation for derivative pricing process. We will also describe the dynamic of our stock price using Binomial lattice model. We also intend to apply Hamilton-Jacobi-Bellman,(HJB) equation to derive the optimal values of our trading strategies. We assume in this paper that the investor is risk averse. Therefore, we adopt an exponential utility function known as Constant Absolute Risk Aversion, (CARA) and maximise the expected final utility function of the investor.