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The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy…
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…
This paper addresses the importance of incorporating various risk measures in portfolio management and proposes a dynamic hybrid portfolio optimization model that combines the spectral risk measure and the Value-at-Risk in the mean-variance…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
This paper considers finitely many investors who perform mean-variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average…
Online portfolio selection research has so far focused mainly on minimizing regret defined in terms of wealth growth. Practical financial decision making, however, is deeply concerned with both wealth and risk. We consider online learning…
In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices…
Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights associated with financial assets held in a…
While the Kelly portfolio has many desirable properties, including optimal long-term growth rate, the resulting investment strategy is rather aggressive. In this paper, we suggest a unified approach to the risk assessment of the Kelly…
We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy. The portfolio strategies rely solely upon second moments. Using a…
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily…
We examine the problem of optimal portfolio allocation within the framework of utility theory. We apply exponential utility to derive the optimal diversification strategy and logarithmic utility to determine the optimal leverage. We enhance…
Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations of asset returns are unstable, and that extremal risk measures such as maximum drawdown are difficult to predict due to…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the…
In this paper, both dynamic mean-variance portfolio selection problems and dynamic variance hedging problems are discussed under non-Markovian framework. Explicit closed-loop equilibrium strategies of these problems are respectively…