Investing in a real world with mean-reverting inflation.

People are concerned about maintaining purchasing power in times of rising inflation. We formulate investment objectives in terms of real wealth, assuming investors derive utility from the number of goods they can buy with their monetary wealth. We derive closed-form solutions for the portfolio choice problem of constant relative risk averse investors, under the assumption that inflation rates are mean-reverting. We consider alternative specifications for the inflation compensation offered by the available assets, in order to study the effect on portfolio choice and welfare. Moreover, we study the added value of inflation-indexed bonds for the investor in our real framework

From boom til bust: how loss aversion affects asset prices

In 1996 Alan Greenspan warned that stock prices were "unduly escalated" and reflected "irrational exuberance". In this paper we describe an economy that can support a prolonged surge of asset prices, accompanied by a sharp increase of volatility. We study an equilibrium model where some agents are risk averse while others have loss averse preferences over wealth, according to prospect theory. We derive closed-form solutions for the equilibrium prices. In good states of the world, the loss averse investors with wealth above the threshold are momentum traders, thereby pushing prices far above the level in the benchmark economy. In moderately bad states of the world, the loss averse investors are contrarian, and equilibrium prices are kept relatively high and stable. Finally in extremely bad states, the loss averse investors are forced to retreat from the stock market in order to avoid bankruptcy, resulting in a sharp price drop

Dynamic asset allocation and downside-risk aversion

This paper considers dynamic asset allocation in a mean versus downside-risk framework. We derive closed-form solutions for the optimal portfolio weights when returns are lognormally distributed. Moreover, we study the impact of skewed and fat-tailed return distributions. We find that the optimal fraction invested in stocks is V-shaped: at low and high levels of wealth the investor increases the stock weight. The optimal strategy also exhibits reverse time-effects: the investor allocates more to stocks as the horizon approaches. Furthermore, the investment strategy becomes more risky for negatively skewed and fat-tailed return distributions

Retirement saving with contribution payments and labor income as a benchmark for investments.

In this paper we study the retirement saving problem from the point of view of a plan sponsor, who makes contribution payments for the future retirement of an employee. The plan sponsor considers the employee's labor income as investment-benchmark in order to ensure the continuation of consumption habits after retirement. We demonstrate that the demand for risky assets increases at low wealth levels due to the contribution payments. We quantify the demand for hedging against changes in wage growth and find that it is relatively small. We show that downside-risk measures increase risk-taking at both low and high levels of wealth

Optimal portfolio choice under loss aversion

Prospect theory and loss aversion play a dominant role in behavioral finance. In this paper we derive closed-form solutions for optimal portfolio choice under loss aversion. When confronted with gains a loss averse investor behaves similar to a portfolio insurer. When confronted with losses, the investor aims at maximizing the probability that terminal wealth exceeds his aspiration level. Our analysis indicates that a representative agent model with loss aversion cannot resolve the equity premium puzzle. We also extend the martingale methodology to allow for more general utility functions and provide a simple approach to incorporate skewed and fat-tailed return distributions

The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between 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 differences and resemblances with the linear programming case

Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for semidefinite programming, our algorithm enjoys the lowest computational complexity

A primal-dual decomposition based interior point approach to two-stage stochastic linear programming

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 that 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 deompostition 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 our model with market prices of options on the S&P500