arXiv research

We solve optimal consumption in a market with bounded risk.

Study resolves duality gap in optimal consumption with random income termination.

We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…

In this paper we study arbitrage theory of financial markets in the absence of a numéraire both in discrete and continuous time. In our main results, we provide a generalization of the classical equivalence between no unbounded profits with bounded risk (NUPBR) and the existence of a supermartingale deflator. To obtain…

Let $\mathbb{F}\subset \mathbb{G}$ be two filtrations and $S$ be a $\mathbb{F}$ semimartingale possessing a $\mathbb{F}$ local martingale deflator. Consider $τ$ a $\mathbb{G}$ stopping time. We study the problem whether $S^{τ-}$ or $S^τ$ can have $\mathbb{G}$ local martingale deflators. A suitable theoretical framework…

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…

Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.

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…

A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is show…

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 numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtrati…

Paper investigates existence of deflators in financial markets.

We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous $g$-supermartingale…

Extended Ville's inequality for nonintegrable supermartingales.

In this paper, we implement a stochastic deflator with five economic and financial risk factors: interest rates, market price of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero-coupon bonds, vanilla options, and corporate cou…

The paper analyzes deflation for estimating a low-rank spike in large tensors with noise.

Constructs supermartingale couplings with full marginals constraints.

Paper optimizes tensor deflation for non-orthogonal signals.

The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk m…

This paper analyzes how errors accumulate in PCA's deflation method.

New inequalities for matrix supermartingales converge under various conditions.

Two probability distributions $μ$ and $ν$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich optimal transport problems where only supermartingales are al…

Sequential tests for nonparametric hypotheses using supermartingales.

The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.

The paper analyzes arbitrage theory in a fluctuating market of stochastic dimension.

We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows…

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of superm…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orth…

Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.

The paper studies optimal maps between hyperbolic surfaces, focusing on their rigidity and obstructions.

DFSOS improves sparse discriminant analysis for high-dimensional data.

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of e…

Study analyzes accuracy of tensor deflation in noisy conditions.

New analysis improves black-box $k$-PCA algorithms, reducing parameter loss.

Given a finite honest time, we first show that the associated Azéma optional supermartingale can be expressed as the drawdown and the relative drawdown of some local optional supermartingales with continuous running supremum. The relative drawdown representation then allows us to provide a characterisation of finite ho…

Study on stability of optimal transport problems for probability measures.

Paper proposes a new deflation varimax method for vintage factor analysis.

No arbitrage in financial markets with special semimartingales.

We investigate default-free bond markets where the standard relationship between a possibly existing bank account process and the term structure of bond prices is broken, i.e. the bank account process is not a valid numéraire. We argue that this feature is not the exception but rather the rule in bond markets when star…

New method deflates manifolds to visualize high-dimensional data.

We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under…

The implementation of conventional sparse principal component analysis (SPCA) on high-dimensional data sets has become a time consuming work. In this paper, a series of subspace projections are constructed efficiently by using Household QR factorization. With the aid of these subspace projections, a fast deflation meth…

Unified framework models multiple financial and insurance term structures.

Bayesian method improves dictionary learning for complex problems.

The paper provides a new uniform tail bound for empirical processes.

Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we translate the property (NFLVR-S) in terms of so called structure conditions and we intr…

A new method inflates and deflates data manifolds to estimate densities without losing universality.