Portfolio Selection in Multidimensional General and Partial Moment Space.

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures suffcient conditions for global optimality. It also forms a natural basis for developing tests on the infuence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirectutility function. This nonparametric effciency measurement framework permits to dfferentiate mainly between portfolio effciency and allocative effciency. Finally, information can,in principle, be inferred about the revealed risk aversion, prudence, temperance and otherhigher-order risk characteristics of investors.shortage function, efficient frontier, K-moment portfolios

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption

The impact of heavy tails and comovements in downside-risk diversification

This paper uncovers the factors influencing optimal asset allocation for downside-risk averse investors. These are comovements between assets, the product of marginal tail probabilities, and the tail index of the optimal portfolio. We measure these factors by using the Clayton copula to model comovements and extreme value theory to estimate shortfall probabilities. These techniques allow us to identify useless diversification strategies based on assets with different tail behaviour, and show that in case of financial distress the asset with heavier tail drives the return on the overall portfolio down. An application to financial indexes of UK and US shows that mean-variance and downside-risk averse investors construct different efficient portfolios.

Asset allocation for pension provision

Financial provision for old age is a serious issue. This paper therefore begins by outlining the pension situation in Germany, arriving at the conclusion that, as matters stand at present, none of the three "pillars" of pension provision - state and occupational pensions and private pension schemes - can sufficiently guarantee adequate retirement income in the future. Given increasing population ageing in Germany for one, provision must focus particularly on fully funded private provisioning and also partly on occupational pension plans. Because of the need for fully-funded systems, asset allocation for pension provision taking account of the key characteristic of retirement saving - the long investment horizon - is particularly important. Thus it is being analysed what effect a varying horizon has on the riskreturn properties of the asset class stocks. The analysis leads to the conclusion that the risk entailed in stock investment is reduced relative to the yield as the investment horizon lengthens. This horizon effect can be put to use for asset allocation, as illustrated with reference to a model based on the shortfall probability (zeroth order lower partial moment, LMP0). A look is also taken at alternative horizon-dependent asset allocation models. The paper concludes with an examination of the practical applicability of the LPM0 for pension provision. --

Does Portfolio Optimization Pay?

All HARA-utility investors with the same exponent invest in a single risky fund and the risk-free asset. In a continuous time-model stock proportions are proportional to the inverse local relative risk aversion of the investor (1/γ-rule). This paper analyses the conditions under which the optimal buy and holdportfolio of a HARA-investor can be approximated by the optimal portfolio of an investor with some low level of constant relative risk aversion using the 1/γ-rule. It turns out that the approximation works very well in markets without approximate arbitrage opportunities. In markets with high equity premiums this approximation may be of low quality.HARA-utility, portfolio choice, certainty equivalent, approximated choice