Transcendental Aspects, Ontological Commitments and Naturalistic Elements in Nietzsche's Thought

Nietzsche's views on knowledge have been interpreted in at least three incompatible ways - as transcendental, naturalistic or proto-deconstructionist. While the first two share a commitment to the possibility of objective truth, the third reading denies this by highlighting Nietzsche's claims about the necessarily falsifying character of human knowledge (his so-called error theory). This paper examines the ways in which his work can be construed as seeking ways of overcoming the strict opposition between naturalism and transcendental philosophy whilst fully taking into account the error theory (interpreted non-literally, as a hyperbolic warning against uncritical forms of realism). In doing so, it clarifies the nature of Nietzsche's ontological commitments, both in the early and the later work, and shows that his relation to transcendental idealism is more subtle than is allowed by naturalistic interpreters while conversely accounting for the impossibility of conceiving the conditions of the possibility of knowledge as genuinely a priori

On Inefficiency of Markowitz-Style Investment Strategies When Drawdown is Important

The focal point of this paper is the issue of "drawdown" which arises in recursive betting scenarios and related applications in the stock market. Roughly speaking, drawdown is understood to mean drops in wealth over time from peaks to subsequent lows. Motivated by the fact that this issue is of paramount concern to conservative investors, we dispense with the classical variance as the risk metric and work with drawdown and mean return as the risk-reward pair. In this setting, the main results in this paper address the so-called "efficiency" of linear time-invariant (LTI) investment feedback strategies which correspond to Markowitz-style schemes in the finance literature. Our analysis begins with the following principle which is widely used in finance: Given two investment opportunities, if one of them has higher risk and lower return, it will be deemed to be inefficient or strictly dominated and generally rejected in the marketplace. In this framework, with risk-reward pair as described above, our main result is that classical Markowitz-style strategies are inefficient. To establish this, we use a new investment strategy which involves a time-varying linear feedback block K(k), called the drawdown modulator. Using this instead of the original LTI feedback block K in the Markowitz scheme, the desired domination is obtained. As a bonus, it is also seen that the modulator assures a worst-case level of drawdown protection with probability one.Comment: This paper has been published in Proceedings of 56th IEEE Conference on Decision and Control (CDC) 201