Related papers: Relative Arbitrage: Sharp Time Horizons and Motion…
We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy…
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…
Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar…
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…
It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks.…
A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy.…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
We argue that the proper time from the horizon to the black hole singularity can be extracted from the thermal expectation values of certain operators outside the horizon. This works for fields which couple to higher curvature terms, so…
The goal of this article is to study minimal surfaces in $\mathbb{M}^2 \times \mathbb{R}$ having finite total curvature, where $\mathbb{M}^2$ is a Hadamard manifold. The main result gives a formula to compute the total curvature in terms of…
Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a…
We give three derivations of Polya's approximation for the expected range of a simple random walk in one dimension. This result allows for an estimation of the volatility of a financial instrument from the difference between the high and…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…