UBC Theses and Dissertations
Dynamic investment models with downside risk control Zhao, Yonggan
Mean-variance analysis has been broadly used in the theory and practice of portfolio management. However, the continuous analogy is not fully studied either academically or in practice. This thesis provides a similar efficient frontier to Markowitz (1952) and a general solution using martingale method employed in Cox and Huang (1989). Comparisons between the expected utility approach and the mean-variance analysis have been made. Traditional utility maximization cannot be used for explicit risk control of downside losses. An adjusted investment objective function by the worst case outcome is incorporated in the investment model. The problem can be divided into two subproblems as in Cox and Huang (1989). Closed form solution is derived for geometric Brownian motion and HARA utility setting. An interesting result is that the investor's decision is governed by a single "security" - a call option on a dynamic mutual fund. A similar strategy, Risk Neutral Excess Return(RNER), to Portfolio Insurance is discussed. With geometric Brownian motion, the RNER strategy has a payoff structure similar to a straddle option strategy. Compare to the strategic asset allocation methods, such as Buy and Hold, Fixed Mix, and Portfolio Insurance , the new approach appears to be superior under a popular risk measure, Value at Risk(VaR). A new objective function is defined for applying stochastic programming to financial investment under uncertainty. Incomplete market conditions are considered in implementing this model. The risk neutral probability is fully studied using stochastic programming techniques.
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