arXiv research

Develops a method to approximate convexity adjustments for interest rate products.

We develop a new method to price SOFR futures contracts considering convexity, skew, and smile.

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX futu…

Investigates concavity of spacetimes, showing conditions for local concavity.

Study shows no closed trapped submanifolds can be tangent to certain spacelike hypersurfaces.

Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.

The study constructs models for SOFR term rates using futures data.

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estim…

The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct violation of the $T-$parity, so that the future-past asymmetry of the physical …

We prove that the topology, smooth structure, and metric of a compact Lorentzian manifold with boundary is uniquely determined by data at the boundary. The data consists of the lengths and directions of future-directed once-broken geodesics connecting points on the boundary, which are first timelike and then lightlike.…

Flat metrics on hyperbolic surfaces embed as polyhedral surfaces in (2+1)-spacetimes.

Anti-de Sitter spacetimes embed cone-metrics as bent Cauchy surfaces.

Investor optimizes stock investments with noisy future price signals.

Proves planarity and convexity for ancient solutions of mean curvature flow.

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who c…

Value functions are crucial for model-free Reinforcement Learning (RL) to obtain a policy implicitly or guide the policy updates. Value estimation heavily depends on the stochasticity of environmental dynamics and the quality of reward signals. In this paper, we propose a two-step understanding of value estimation from…

The paper extends Reshetnyak's theorem to Lorentzian length spaces with upper curvature bounds.

We investigate the problem of pricing and hedging derivatives of Electricity Futures contract when the underlying asset is not available. We propose to use a cross hedging strategy based on the Futures contract covering the larger delivery period. A quick overview of market data shows a basis risk for this market incom…

The online meta-learning framework is designed for the continual lifelong learning setting. It bridges two fields: meta-learning which tries to extract prior knowledge from past tasks for fast learning of future tasks, and online-learning which deals with the sequential setting where problems are revealed one by one. I…

No accelerated gradient method for hyperbolic convex functions.

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…

Let $S$ be a compact, orientable surface of hyperbolic type. Let $(k_+,k_-)$ be a pair of negative numbers and let $(g_+, g_-)$ be a pair of marked metrics over $S$ of constant curvature equal to $k_+$ and $k_-$ respectively. Using a functional introduced by Bonsante, Mondello \& Schlenker, we show that there exists a …

Optimizes risk-neutral probabilities for derivative pricing.

PredPCA extracts key components for better time series prediction.

The paper tackles performative risk optimization under weak convexity assumptions.

It is known that the space of convex polygons in the Euclidean plane with fixed normals, up to homotheties and translations, endowed with the area form, is isometric to a hyperbolic polyhedron. In this note we show a class of convex polygons in the Lorentzian plane such that their moduli space, if the normals are fixed…

This paper optimizes performative risk by focusing on convex properties and developing efficient algorithms.

We show that for a very general and natural class of curvature functions (for example the curvature quotients $(σ_n/σ_l)^{\frac{1}{n-l}}$) the problem of finding a complete spacelike strictly convex hypersurface in de Sitter space satisfying $f(κ) = σ\in (1,\infty)$ with a prescribed compact future asymptotic boundary …

Study on optimizing model updates in performative prediction.

The paper constructs convex subsets in anti-de Sitter space with specific metrics on boundaries.

We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these matchings to classify every subcomplex whose reduced homology groups are concentra…

Low-rank forecasting improves consistency in time series predictions.

Study Gromov hyperbolic domains in Minkowski space, proving equivalence to boundary properties.

AA extracts archetypes from data for clear feature extraction.

This paper reviews techniques for distributed learning with non-convex models.

The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the boundary. This approach is in a sense dual to using derivatives of the volume i…

New algorithms find near-stationary points in convex optimization.

We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of minimizing/maximizing certain ris…

New framework uses tempered optimism to handle imperfect experts in online learning.

Study of curvature flow in Minkowski space converging to a hyperboloid.

We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask: \textit{under what general conditions is it possible for an online learner to leverage predictions of futur…

Consider an agent taking two successive decisions to maximize his expected utility under uncertainty. After his first decision, a signal is revealed that provides information about the state of nature. The observation of the signal allows the decision-maker to revise his prior and the second decision is taken according…

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and h…

Paper examines financial engineering problems and introduces AlphaZero for better replication strategies.

We introduce a particular class of unbounded closed convex sets of $\R^{d+1}$, called F-convex sets (F stands for future). To define them, we use the Minkowski bilinear form of signature $(+,...,+,-)$ instead of the usual scalar product, and we ask the Gauss map to be a surjection onto the hyperbolic space $\H^d$. Impo…

Optimal domain adaptation model using Fisher's Linear Discriminant.

Survey of advances in non-convex min-max optimization for applications.

The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.