We use a log-normal framework to examine the effect of preferences on the market price for risk, that is, the Sharpe ratio. In our framework, the Sharpe ratio can be calculated directly from the elasticity of the stochastic discount factor with respect to consumption innovations as well as the volatility of consumption innovations. This can be understood as an analytical shortcut to the calcula...

We consider an investor who seeks to maximize her expected utility derived from her terminal wealth relative to the maximum wealth achieved over a fixed time horizon, and under a portfolio drawdown constraint, in a market with local stochastic volatility (LSV). The newly proposed investment objective paradigm also allows the investor to set portfolio benchmark targets. In the absence of closed-...

We describe a general method to transform a non-Markovian sequential decision problem into a supervised learning problem using a K-bestpaths algorithm. We consider an application in financial portfolio management where we can train a controller to directly optimize a Sharpe Ratio (or other risk-averse non-additive) utility function. We illustrate the approach by demonstrating experimental resul...

The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as a byproduct a new understanding of the means of returns, of the beta coefficient, and of the Sharpe and Treynor ratios. New estimation techniques from automa...

Independent risks are substitutes if the opportunity to invest in one risk cuts down the demand in the others. Intuition seems to sustain this idea, but if the problem is tackled in a normative framework, no consensus in the literature is found. In this paper we investigate what does happen if the decision rule is based on the Generalized Sharpe Ratio. The answer depends on the risk measure und...

Optimal asset allocation well-fitting the investors goals is a pressing challenge in risk management. In spite of Sharpe ratio, Sortino-Satchell, Generalized Rachev and Farinelli-Tibiletti ratios are new parameter-dependent performance ratios able to suit the investor risk profile. Five investor prototypes are studied and fifteen tailormade optimal asset paths are traced over a rolling twelve m...