Optimal Asset Allocation with Minimum Guarantees

Abstract

本研究中，考慮連續時間下，附最低保證之長期最適投資策略；在利率模型中，為較能符合現實狀況，我們採用CIR模型；另外，在此策略中，我們將投資人之風險偏好加入模型中研究，最適化投資人到期時財富之效用函數，並用Cox & Huang之市場中立評價方法來解決數學模型問題。此篇研究顯示，最適之投資策略可以等價於某些共同基金之投資組合，這些共同基金能利用金融市場上之主要資產(market primary assets)來複製。

In this study, we consider a portfolio selection problem for long-term investors. Dynamic investment\nstrategy with the continuous-time framework incorporating the minimum guarantees are\nconstructed. Maximizing expected utility of the terminal wealth is employed by investors to trade\noff profits in good future state against losses incurred in worse states. Follow the previous works\nof Deelstra et al. (2003), we concentrate on the simplest case of a one-factor Cox-Ingersoll-Ross\n(CIR) model in formulating the stochastic variation from the interest rate risks. Under the market\ncompleteness assumption, the fund growth is modelled under the market neutral valuation and\nthe optimal rules are mapped into the static variational problem of Cox and Huang (1989). In\nthis study, we show that the optimal portfolio is equivalent to a certain mutual fund that can be\nreplicated by the market primary assets