Purpose – The purpose of this paper is to find the optimal hedging strategy when an investor has budget constraints on both the initial capital and the future cash flow. Design/methodology/approach – The paper follows the utility minimization of the total cost, using convex utility functions on both initial capital and future cash flows. Findings – Closed-form solutions of optimal hedging strategies are found in some specific but popular cases. It is also found that this method corresponds to the local risk minimization method in quadratic hedging. Research limitations/implications – Hedging strategies are calculated for only two popular choices. One may want to calculate hedging strategies for other popular utility functions such as power utility or HARA utility. Practical implications – When a trader has some budget constraint in both initial capital and future cash flows, this paper gives a simple alternative. Originality/value – Budget constraints on both initial capital and future cash flow are new to this kind of study. Connection to the local risk minimization strategy is original too.
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