Financial Mathematics

Phynance ArXiv ID: ssrn-2433826 “View on arXiv” Authors: Unknown Abstract These are the lecture notes for an advanced Ph.D. level course I taught in Spring ‘02 at the C.N. Yang Institute for Theoretical Physics at Stony Brook. The cou Keywords: Stochastic Processes, Financial Mathematics, Brownian Motion, Derivatives Pricing, Derivatives Complexity vs Empirical Score Math Complexity: 9.0/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper is a PhD-level lecture on advanced stochastic calculus and derivative pricing, heavily featuring formal mathematical derivations and physics-inspired path integral methods, but contains no empirical data, backtests, or implementation details. flowchart TD A["Research Goal: Model Derivatives Pricing via Stochastic Processes"] --> B["Key Methodology: Applied Brownian Motion & Itô Calculus"] B --> C["Data/Inputs: Financial Market Parameters & Hypothetical Models"] C --> D["Computational Process: Solving Stochastic Differential Equations"] D --> E["Outcome: Analytical Derivatives Pricing Frameworks"]

European Football Player Valuation: Integrating Financial Models and Network Theory ArXiv ID: 2312.16179 “View on arXiv” Authors: Unknown Abstract This paper presents a new framework for player valuation in European football, by fusing principles from financial mathematics and network theory. The valuation model leverages a “passing matrix” to encapsulate player interactions on the field, utilizing centrality measures to quantify individual influence. Unlike traditional approaches, such as regressing on past performance-salary data, this model focuses on in-game performance as a player’s contributions evolve over time. Consequently, our model provides a dynamic and individualized framework for ascertaining a player’s fair market value. The methodology is empirically validated through a case study in European football, employing real-world match and financial data. This cross-disciplinary mechanism for player valuation adapts the effect of connecting pay with performance, first seen in Scully (1974), to include in-game contributions as well as expected present valuation of stochastic variables. ...

A generalization of the rational rough Heston approximation ArXiv ID: 2310.09181 “View on arXiv” Authors: Unknown Abstract Previously, in [“GR19”], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel. In this paper we extend this solution to the general case of the Mittag-Leffler kernel with λ\geq 0. We provide numerical evidence of the convergence of the solution. ...