This paper analyzes the optimal investment strategy for loss averse investors, assuming a complete market and general Ito processes for the asset prices. The loss-averse investor follows a partial portfolio insurance strategy. When the investor's planning horizon is short (less than 5 years), he or she considerably reduces the initial portfolio weight of stocks compared to an investor with smooth power utility. The empirical section of the paper estimates the level of loss aversion implied by historical U.S. stock market data, using a representative agent model. We find that loss aversion and risk aversion cannot be disentangled empirically. © 2004 President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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In this chapter we describe the optimal set approach for sensitivity analysis for LP. W e show that optimal partitions and optimal sets remain constant b e t w een two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach using optimal bases is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss di erences and resemblances with the linear programming case.

Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties which has found applications in, e.g., finance, such as asset-liability and bond-portfolio management. Computationally, however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. For a model to be well solvable, its special structure must be explored. Most of the solution methods are based on decomposing the data. In this paper we propose a new decomposition approach for two-stage stochastic programming, based on a direct application of the path-following method combined with the homogeneous self-dual technique. Numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs. In particular, we apply our decomposition method to a two-period portfolio selection problem using options on a stock index. In this model the investor can invest in a money-market account, a stock index, and European options on this index with different maturities. We experiment with our model with market prices of options on the S&P500.

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