This paper extends Merton’s continuous time (instantaneous) mean-varianceanalysis and the mutual fund separation theory. Given the existence of a Marko-vian state price density process, the optimal portfolios from concave utility max-imization are instantaneously mean-variance efficient...

This paper considers the problem of investment of capital in risky assets in adynamic capital market in continuous time. The problem addressed is the control of risk, and in particular the risk associated with errors in the estimation of returns on assets. The framework for investment risk is a...

Financial disasters to hedge funds, bank trading departments and individual speculative traders and investors seem to always occur because of non-diversification in all possible scenarios, being overbet and being hit by a bad scenario. Black swans are the worst type of bad scenario: unexpected...