A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops a martingale expansion for stochastic volatility models.
Conic martingales refer to Brownian martingales evolving between bounds. Among other potential applications, they have been suggested for the sake of modeling conditional survival probabilities under partial information, as usual in reduced-form models. Yet, conic martingale default models have a special feature; in co…
We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum entropy martingale measure for stochastic volatility models of Ornstein-Uhlenbe…
The paper studies projections of asset prices under equivalent martingale measures.
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular, we derive conditions for the existence of the minimal martingale measure. We al…
A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven…
We extend Kyle's model to include stochastic liquidity and multiple assets.
New algorithm selects robust martingale for optimal stopping problems.
There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between th…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…
In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations…
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, -optimal martingale measures, bilateral Esscher…
Study on martingale property and moment explosions in signature volatility models.
Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.
The paper describes how martingales can be represented after a random time in financial models.
We prove the existence and uniqueness of solutions of SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. The main tool in our reasoning is Picard's iterative procedure and a model-free version of the Burkholder-Davis-Gundy inequality for integrals driven by model-free, continuous martingale…
In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a…
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
In the "positive interest" models of Flesaker-Hughston, the nominal discount bond system is determined by a one-parameter family of positive martingales. In the present paper we extend this analysis to include a variety of distributions for the martingale family, parameterised by a function that determines the behaviou…
Investigates model risk and semi-static hedging for martingale constrained models.
Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatović and Urusov (2012c) give necessary and sufficient conditions in the case of perfect correlation (ρ=1).…
We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller informatio…
In credit risk literature, the existence of an equivalent martingale measure is stipulated as one of the main assumptions in the hazard process model. Here we show by construction the existence of a measure that turns the discounted stock and defaultable bond prices into martingales by identifying a no-arbitrage condit…
Unique solutions found for diffusive martingale problems.
Study optimal semistatic portfolios using martingale Schrödinger bridges.
Quantum probability theory constructs Martingales for non-Brownian financial models.
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale…
We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. Th…
Existence proved for -Bass martingales with specific marginals.
Study finds optimal martingale coupling between two distributions with minimal entropy.
New analysis shows LLMs don't follow Bayesian inference in ICL.
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the rec…
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the disc…
Note on failure of Martingale Wasserstein Inequality in higher dimensions.
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant chang…
Score-based martingale posteriors improve uncertainty quantification in deep neural networks.
Study uses viscosity solutions to solve control problems involving measure-valued martingales.
The paper shows how to construct non-Gaussian Martingales using hyperbolic diffusion.
The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectat…
Extends optimal transport to dynamic and martingale settings.
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…
Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.
We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form with being a stochastic volatility term.
We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a chan…
Dual martingales improve primal optimal stopping problem efficiency.
A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a p…