A Comparison Between Goal Reaching and Yaari's Models
In this project we build on the work done by He and Zhou in their paper Portfolio Choice via Quantiles[3]. We first explain in brief their portfolio choice model for the complete markets and the solution to the Goal Reaching problem and Yaari's model. We study the effect of Sharpe ratio on the...
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| Format: | Thesis |
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Mathematical Institute;University of Oxford
2009
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| Summary: | In this project we build on the work done by He and Zhou in their paper Portfolio Choice via Quantiles[3]. We first explain in brief their portfolio choice model for the complete markets and the solution to the Goal Reaching problem and Yaari's model. We study the effect of Sharpe ratio on the two and are able to analytically prove that for the Goal Reaching Model an increase in Sharpe ratio increases the probability of achieving the target. We study in depth a concrete example of a particular distortion function - the power function in the Yaari's model. We calibrate the Goal Reaching problem and the Yaari's model with power function as probability distortion to the Dow Jones Industrial Average and show the probabilities of achieving targets under the two models. We also compare the results from the two models when given the same targets, in the same time horizon. Finally we show that the Goal Reaching problem can be embedded within the Yaari's model for a particular class of probability distortion functions and under this framework the Goal Reaching problem is risk averse. |
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