About 13 years ago, my friend Eric Remole, who was at the time a quant working for Chancellor Capital Management in Manhattan, introduced me to "neural networks." This is a type of computational model (of a handful of types) based on the self-organizing modes of adaptation found in living systems at every scale. Neural networks are modeled specifically on the processing characteristics of networks of neurons in any life-form complex enough to have developed specialized nervous tissue distinct, in both form and function, from other tissues.
As a psychiatrist with a longstanding interest in both neuroscience and physics, I was immediately hooked: By mimicking nature, neural nets could both accomplish much that had evaded standard computer architecture and provide the working models for brain function.
Neural network theory, I learned, wasn't at all new: John von Neumann, whose work inspired Nobel prizes in seven distinct disciplines, was long a proponent of them, as also of related forms of "artificial life." But neural networks had been exiled to the academic thorn-forest by a premature "proof" that they were mathematically "sterile," until re-awakened by John Hopfield, a Princeton condensed-matter theoretical physicist. In an electrifying 1982 presentation at the National Academy of Sciences, mostly to physicists, Hopfield showed that certain (even) inorganic substances called spin-glasses could spontaneously form memories, store them "associatively" and then recall them to recognize even imperfect patterns: just the way that our own cognizing of pattern is stored and, in recognition, retrieved.
The human brain is especially good at extracting underlying patterns from a sea of noise, where standard computers are not--for instance, in guessing investment strategies. It didn't take long for the major financial houses around the world (but especially in Japan) to begin applying neural networks to market and financial forecasting.
My own interest in neural nets was (and remains) primarily scientific, but not entirely. I read everything I could on the subject, took some (private) courses held at Carnegie-Mellon by a group of neural network pioneers who had founded a company devoted to the technology, and began (1) a long period of study and reflection that culminated in my recent book, The Quantum Brain (2) an equally long period of development of combined neural-network, genetic algorithm and non-parametric statistical and statistical physics-based models for hedged investment strategies.
On the strictly scientific side, I am now pursuing a PhD in theoretical "condensed matter" physics at Yale, where my advisors are Steven Girvin and David deMille. Steve's own advisor at Princeton, where he did his Ph.D., was John Hopfield. My area of specialization is quantum information theory (including quantum computation), but I have an eye on applying adaptive systems (including neural networks, but not only) to the search for useful quantum information processing algorithms. Dave and his group are deep into the construction of a 4,000 (!) qubit computation device based on the entangled quantum states of trapped, ultra-cold heteronuclear molecules.
On the financial side, I became the quantitative partner for a small ("boutique") hedge fund advisory based in Westport, Connecticut. We apply adaptive-systems methods to the selection and trading of baskets of financial instruments, some relatively long-, some relatively short-term. Using these methods, we've devised strategies that make good returns with low measurements of risk. Our continuing development is focused on preserving these returns while achieving ever lower levels of both overall and component-wise volatility, as measured on both a short- and long-term basis.
A major focus of my quantitative finance research and model-development is risk, in particular, the application to price (and value) "trajectories" of certain new (extraordinarily powerful) tools of mathematical physics, so as to define volatility more realistically and therefore to apply it more effectively not only for portfolio composition, but prospectively as well: On average, the anticipated "risk" of an investment is, after all, the single largest determining factor in its subsequent price, that is to say, of its own volatility!
The self-iterating character of most real-world physical systems, and all financial ones, is just what make them so difficult usefully to quantify, model and predict--however apparent the underlying order.
The graphic image above illustrates this point: It is, in fact, an iterated trajectory; each of its points (apart from a randomly selected first one but including points of every color as well as those on the apparent "grid") was generated by a previous one. But were you to number the points as they're generated, not a single point "n+1" would be found immediately next to point "n", and the vast majority of "n+1"s would be more than 1/4 the image-width away from their "n"s. Indeed, were you to connect with a line every disconnected point to its successor, the figure would look like a total mess. Go figure.
I am especially pleased to be working with Ken Von Kohorn, a fund manager with an outstanding track record over nearly thirty years, who is equally pleased to allow me to function as the backroom nerd. For the title of most nerd-like I have to compete, however, with his nephew, Daniel Von Kohorn, who recently joined us to manage (among other matters) our portfolio-composing activities.