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Benoit Mandelbrot's scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a "fox" in Isaiah Berlin's famous dichotomy of thinkers. This essay argues, however, that Mandelbrot was, at heart, a "hedgehog": a thinker unified by a single guiding principle. Across his diverse pursuits, the concept of scaling…
We suggest an original physical approach to describe the mechanism of market pricing. The core of our approach is to consider pricing at different time scales separately, using independent equations of motion. Such an approach leads to a pricing model that not only allows estimating the volatility of future market prices, but also permits forecasting the direction of the price move. Alongside with that, it is crucial…
We study a multi-agent setting in which brokers transact with an informed trader. Through a sequential Stackelberg-type game, brokers manage trading costs and adverse selection with an informed trader. In particular, supplying liquidity to the informed traders allows the brokers to speculate based on the flow information. They simultaneously attempt to minimize inventory risk and trading costs with the lit market bas…
This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original a…
We propose a new approach to model rainfall by combining heterogeneous data sources at different time scales. Continuous arrivals of rain cells are incorporated into a Hawkes process formalism that encompasses the classical Bartlett-Lewis and Neyman-Scott models, thereby providing a more flexible representation of clustering. Analysis of high frequency rainfall data (at the minute scale over several years) indicates …
A VAE is a probabilistic autoencoder: the encoder outputs a distribution q(z|x), the decoder p(x|z), and training maximizes an ELBO with a KL term that keeps the latent well-behaved.
A liquidity trap is a state where the policy rate is at or near the effective lower bound and extra money is hoarded rather than spent, so conventional rate cuts stop working.