A recent line of work has studied the statistical properties of neural networks to great success from a mean field theory perspective, making and verifying very precise predictions of neural network behavior and test time performance. In this paper, we build upon these works to explore two methods for taming the behaviors of random residual networks (with only fully connected layers and no batc...

Classical derivations of mean variance preferences have all relied upon the expected utility hypothesis. Some widespread experimental studies have uncovered that the expected utility model tends to be systematically violated in practice. Such findings would lead people to doubt the empirical relevance of the literature and the practical effectiveness of the portfolio selection which employ the ...

5 We present efficient partial differential equation (PDE) methods for continuous time mean6 variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. 7 The standard formulation of mean-variance optimal portfolio allocation problems, where the 8 total wealth is the underlying stochastic process, gives rise to a one-dimensional (1-D) non-linear 9 Hamilton-J...

We analyze comparative static effects under uncertainty when a decision maker has mean-variance preferences and faces a generic, quasi-linear decision problem with both an endogenous risk and a background risk. In terms of mean-variance preferences, we fully characterize the effects of changes in the location, scale, and concordance parameters of the stochastic environment on optimal risk-takin...

The widely accepted belief that asset returns and insurance product line margins are not normally distributed has motivated the use of skewness (or higher than second order moments), in the context of optimal risk-reward portfolio allocation. Here, we propose an optimization-based methodology to substantially improve the skewness of portfolios in the mean-variance efficient frontier. Unlike oth...

The results on the mean-variance hedging problem in Gouriéroux, Laurent and Pham (1998), Rheinländer and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the numéraire method is used, we only assume the Radon-Nikodym derivative of the variance-optimal signed martingale measure (VSMM) is non-zero almost surely (but may be strictly negative). When discuss...