On the Payoff Valuations of Investment Strategies: A Case of Multiple Investment Companies

Abstract

We consider the payoff valuation of an investor for investing in N  investment companies. The investor paid some percentage as cost of running the investment to the investment companies. Since stock price is naturally random over time, we assume that it follows a standard geometric Brownian motion with a consumption process Λ_t,0 ≤t≤T  which is a nonnegative and F - adapted process such that ∫₁^t Λ_tdt<∞. This consumption process is the sum total amount consumed by the investment companies from time period t=0 to time period T on behalf of the investor. We are to maximize the investor’s investment in N companies. We also determine among the companies, which of them yield the highest returns at time t. We find that investors may not invest in some of the companies as a result of poor performance that arises from the high risk involve in the investments.

Keywords: Payoff valuation; Investment strategy; Stock price; Stochastic.