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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…
This work derives an approximate analytical single period solution of the portfolio choice problem for the power utility function. It is possible to do so if we consider that the asset returns follow a multivariate normal distribution. It…
Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in markets based on…
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this…
In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered…
We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility…
This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective…
Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and…
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…
A {log-optimal} portfolio is any portfolio that maximizes the expected logarithmic growth (ELG) of an investor's wealth. This maximization problem typically assumes that the information of the true distribution of returns is known to the…
In this paper, we consider a frequency-based portfolio optimization problem with $m \geq 2$ assets when the expected logarithmic growth (ELG) rate of wealth is used as the performance metric. With the aid of the notion called dominant…
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…
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility…
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic…
This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the…