arXiv research

We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption, which restricts the variability of the forward-looking transitions of the martingal…

Study detects concept shift in online data using martingales.

Develops European power option pricing under correlated interest rate and asset processes.

New method finds closest martingale to Brownian motion.

Dynamic reinsurance aims to minimize surplus risk using martingale transport.

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…

We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then endogenously as full support martingale measures (instead of equivalent martingale…

Time series forecasting is widely used in a multitude of domains. In this paper, we present four models to predict the stock price using the SPX index as input time series data. The martingale and ordinary linear models require the strongest assumption in stationarity which we use as baseline models. The generalized li…

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…

Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.

Score-based martingale posteriors improve uncertainty quantification in deep neural networks.

Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…

The paper describes how martingales can be represented after a random time in financial models.

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…

Study Nash equilibrium in mean field portfolio games with random market parameters.

In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale…

New bounds on self-normalized martingales improve online linear regression performance.

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

Paper proves convergence of SA algorithm via martingale and converse Lyapunov methods.

We consider the problem of quickest change-point detection in data streams. Classical change-point detection procedures, such as CUSUM, Shiryaev-Roberts and Posterior Probability statistics, are optimal only if the change-point model is known, which is an unrealistic assumption in typical applied problems. Instead we p…

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …

We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In…

This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.

Volterra square-root process boundary behavior and martingale measures

Let $\mathbb{Q}$ and $\mathbb{P}$ be equivalent probability measures and let $ψ$ be a $J$-dimensional vector of random variables such that $\frac{d\mathbb{Q}}{d\mathbb{P}}$ and $ψ$ are defined in terms of a weak solution $X$ to a $d$-dimensional stochastic differential equation. Motivated by the problem of \emph{endoge…

We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption that the increments of the asset price are independent conditionally on the factor…

We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, althou…

Identifies bilinear systems from a single trajectory with optimal sample complexity.

When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the literature by deriving sufficient conditions for the existence of …

New algorithm selects robust martingale for optimal stopping problems.

Investigates a Kyle model with imperfect information and risk aversion.

We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $\mathcal{P}$ nor on the structure of the state space. Several aspects of modeling under Knightian Uncer…

Adaptive monitoring for AI systems detects and diagnoses shifts in data distribution.

Develops a martingale expansion for stochastic volatility models.

The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…

We develop time-uniform confidence spheres for estimating means of random vectors.

Enhances MOT with causality constraints for better option pricing.

Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.

A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of t…

The paper studies horizontal semimartingales on Riemannian manifolds and their connections to Euclidean spaces.

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, …

Study improves off-policy evaluation from non-i.i.d. bandit samples.

DeepMartingale uses deep learning to solve complex optimal stopping problems efficiently.

Improved bounds for proximal gradient algorithms with computational errors.

ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and white ass…

Existence proved for $q$-Bass martingales with specific marginals.

Paper studies pricing and hedging of nonreplicable insurance contracts using benchmark-neutral approach.

Study finds optimal martingale coupling between two distributions with minimal entropy.