We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuous-time version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the first-order conditions of optimality as a system of forward backward SDEs, which, in the Markovian case, red...

We consider a large trader seeking to liquidate a portfolio using both a transparent trading venue and a dark pool. Our model captures the price impact of trading in transparent traditional venues as well as the execution uncertainty of trading in a dark pool. The unique optimal execution strategy uses both venues continuously. The order size in the dark pool can overor underrepresent the portf...

Starting from the reward-risk model for portfolio selection introduced in De Giorgi (2004), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. The reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on few basic principles, including consistency with second order stochastic dominance. Wi...

We examine the optimal trading strategy for a CRRA investor who maximizes the expected utility of wealth on a finite date and faces transaction costs. Closed-form solutions are obtained when this date is uncertain. We then show a sequence of analytical solutions converge to the solution to the problem with a deterministic finite horizon. Consistent with the common life-cycle investment advice, ...

Sequential portfolio selection has attracted increasing interest in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision-making under uncertainty, namely the exploration versus exploitation dilemma, and therefore...

This paper deals with a portfolio selection problem based on the possibility theory under the assumption that the returns of assets are LR-type fuzzy numbers. A possibilistic portfolio model with transaction costs is proposed, in which the possibilistic mean value of the return is termed measure of investment return, and the possibilistic variance of the return is termed measure of investment r...

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce “uncertainty structures” for the market parameters and show that the robust portfolio selection pro...

The mean-variance-leverage (MVL) optimization model (Jacobs and Levy [2012, 2013]) tackles an issue not dealt with by the mean-variance optimization inherent in the general mean-variance portfolio selection model (GPSM) — that is, the impact on investor utility of the risks that are unique to using leverage. Relying on leverage constraints with a conventional GPSM, as is commonly done today, is...

this paper discusses the portfolio selection based on robust optimization. since the parameters values of the portfolio optimization problem such as price of the stock, dividends, returns, etc. of per share are unknown, variable and their distributions are uncertain because of the market and price volatility, therefore, there is a need for the development and application of methodologies for de...

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce “uncertainty structures” for the market parameters and show that the robust portfolio selection pro...