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In its capacity as debt issuer, the state has played a growing role in financial life over the last 30 years. To examine this role and connect it to shadow banking, the paper develops the concept of the ‘repo trinity’, which captures a set of policy objectives that central banks outlined after the 1998 Russian crisis, the first systemic crisis of collateral-based finance. The repo trinity connected financial stabilit…
Concentrated-liquidity automated market makers (CLAMMs), as exemplified by Uniswap v3, are now a common primitive in decentralized finance frameworks. Their design combines continuous trading on constant-function curves with discrete tick boundaries at which liquidity positions change and rounding effects accumulate. While there is a body of economic and game-theoretic analysis of CLAMMs, there is negligible work tha…
A heat kernel approach is proposed for the development of a general, flexible, and mathematically tractable asset pricing framework in finite time. The pricing kernel, giving rise to the price system in an incomplete market, is modelled by weighted heat kernels which are driven by multivariate Markov processes and which provide enough degrees of freedom in order to calibrate to relevant data, e.g. to the term structu…
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…
The present work addresses the challenge of training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk, a task traditionally burdened by the high costs associated with generating training datasets through nested Monte Carlo (MC) simulations. By condensing the initial market state variables into an input vector, determined through an interest rate model and a parsimonious paramet…
The introduction of CCPs in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according to the TABB group, will lead to an overall liquidity impact about 2 USD trillions. In this article we develop for the first time a comprehensive approach for pricing under CCP clearing, including variation and initial margins, gap credit risk and collatera…
Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of correlated time series. We develop our …
Portfolio optimization under strict cardinality constraints is a combinatorial challenge that defies classical convex optimization techniques, particularly in the context of "Direct Indexing" and ESG-constrained mandates. In the Noisy Intermediate-Scale Quantum (NISQ) era, the Quantum Approximate Optimization Algorithm (QAOA) offers a promising hybrid approach. However, standard QAOA implementations utilizing transve…
In this article we present a novel and general methodology for building second order finite volume implicit-explicit (IMEX) numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. In particular, applications to basket and Heston models are presented. The obtained numerical schemes have excellent properties and are able to overcome the well-documented difficulties related with nu…
Central clearing counterparty houses (CCPs) play a fundamental role in mitigating the counterparty risk for exchange traded options. CCPs cover for possible losses during the liquidation of a defaulting member's portfolio by collecting initial margins from their members. In this article we analyze the current state of the art in the industry for computing initial margins for options, whose core component is generally…
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the finite-difference solution from one dimension, to be used in linear regression. This approach bridges between solving backward partial differential equations and Monte Carlo simulation, aimi…
This study examines the impact of dividend policy on the performance of initial public offerings in India. The period of study is from the year 2011-2014. Monthly returns of the IPOs issued in the considered period and the Indian Stock Market Index (Nifty 50) were considered for the long-run performance study. The methodological tools used are long-run performance statistics and the GARCH model. The Dummy variable wa…
This paper presents the Runge-Kutta-Legendre finite difference scheme, allowing for an additional shift in its polynomial representation. A short presentation of the stability region, comparatively to the Runge-Kutta-Chebyshev scheme follows. We then explore the problem of pricing American options with the Runge-Kutta-Legendre scheme under the one factor Black-Scholes and the two factor Heston stochastic volatility m…
We study the behavior of linear discriminant functions for binary classification in the infinite-imbalance limit, where the sample size of one class grows without bound while the sample size of the other remains fixed. The coefficients of the classifier minimize an empirical loss specified through a weight function. We show that for a broad class of weight functions, the intercept diverges but the rest of the coeffic…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change from its current value. We consider an incomplete stochastic volatility market model, that is driven by both a Brownian motion and a jump process. At first, we obtain a closed-form…
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or maturity which comes earlier. The company is allowed to buy reinsurance contracts dynamically over the whole time horizon to cede its risk exposure with other reinsurance companies.…
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible beca…
Xavier/Glorot initialization scales initial weights so variance is preserved through a layer — the default that made deep tanh/sigmoid nets trainable before BatchNorm.
The Coase theorem says that if property rights are clear and bargaining is costless, parties will bargain to an efficient outcome regardless of who holds the initial right — the assignment affects distribution, not efficiency.
The impossible trinity (trilemma) says a country cannot simultaneously have a fixed exchange rate, free capital mobility, and an independent monetary policy — it must drop one.
An IPO is a private firm’s first sale of stock to public investors — a liquidity and valuation event, not a proof of quality.
Initial Margin Procyclicality — Margin models that rise sharply in stress and amplify deleveraging.
The central limit theorem says that sums of many independent, finite-variance shocks look Gaussian — which is why so many models start with a normal, and why they fail when those assumptions fail.
The central limit theorem says that sums of many independent, finite-variance shocks look Gaussian — which is why so many models start with a normal, and why they fail when those assumptions fail.
The Coase theorem says that if property rights are clear and bargaining is costless, parties will bargain to an efficient outcome regardless of who holds the initial right — the assignment affects distribution, not efficiency.
The impossible trinity (trilemma) says a country cannot simultaneously have a fixed exchange rate, free capital mobility, and an independent monetary policy — it must drop one.
Initial Margin Procyclicality — Margin models that rise sharply in stress and amplify deleveraging.
An IPO is a private firm’s first sale of stock to public investors — a liquidity and valuation event, not a proof of quality.
Xavier/Glorot initialization scales initial weights so variance is preserved through a layer — the default that made deep tanh/sigmoid nets trainable before BatchNorm.