arXiv research

Investigates a new measure PELVE_n for risk assessment.

A new method for calculating ES from VaR under Solvency II.

Extended PELCoV for bivariate Student-t copulas to monitor foreign exchange risk.

Let $A \subset \mathbb{R}^d$, $d\ge 2$, be a compact convex set and let $μ= \varrho_0 dx$ be a probability measure on $A$ equivalent to the restriction of Lebesgue measure. Let $ν= \varrho_1 dx$ be a probability measure on $B_r := \{x\colon |x| \le r\}$ equivalent to the restriction of Lebesgue measure. We prove that t…

We study a family of polynomials in two variables having moduli up to bilipschitz equivalence: two distinct polynomials of this family are not bilipschitz equivalent. However any level curve of the first polynomial is bilipschitz equivalent to a level curve of the second.

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive t…

The paper proposes a new method for comparing logistic regression models across different populations.

Generative model learns conditional distributions on collective variable levels.

We determine the optimal strategy for investing in a Black-Scholes market in order to maximize the probability that wealth at death meets a bequest goal $b$, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965, 1976). The individual consumes at a constant rate $c$, so the level of wealth required fo…

New bounds for LDP with heterogeneous privacy levels guaranteeing high probability of accuracy.

New Fourier metrics equivalent to Wasserstein distances in image processing.

Investigates multi-period portfolio optimization for DC plans using buffered Probability of Exceedance.

Paper speeds up visualization of uncertain data.

This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the numéraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the…

The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent p…

Characterizes measures preserving compound mixed renewal process properties.

In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Ka…

"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We giv…

This paper applies quantum probability theory to model asset returns, avoiding assumptions about quantum effects.

We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classes. These new invariants are as simple, but more discerning than existing topological invariants, such as persistence barcodes and Reeb graph…

New scoring rules for multivariate distributions and level sets.

Sequence probability predicts correctness in LLMs, but not for repeated prompts

Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.

The paper analyzes fill probabilities in limit order books with varying price levels.

We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation probabilities, 2) the level crossing probabilities, and 3) the level crossing probabilities…

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

Near-optimal tests and confidence sequences for non-parametric data.

Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent a big data set as a set of non-overlapping data subsets, called RSP data blocks,…

This paper calibrates distribution models from PELVE values.

We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between probability measures, is not significantly easier than estimating the probabili…

Optimizes latency and false alarm probability in change detection problems.

Handlebody groups are rigid under measure equivalence.

The level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, $ν_α^+$, where $T_α =1/ν_α^+$ is the average waiting time for observing the level $α$ again. We estimate the probability $P(K, α)$, which provides us the probab…

ESRLCM clusters similar responses, more broadly than traditional models.

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of arbitrage and the existence of an equivalent martingale measure is a folk theorem,…

Since the 1960s, the question whether markets are efficient or not is controversially discussed. One reason for the difficulty to overcome the controversy is the lack of a universal, but also precise, quantitative definition of efficiency that is able to graduate between different states of efficiency. The main purpose…

We shrink confidence sets for equivalent discrete distributions using permutation equivalence.

Models predict probabilities of causation from limited data.

We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income…

Proposes a new framework to manage venture capital portfolio risk by focusing on deal-level correlations.

Study graph products of groups, classifying them up to measure equivalence and rigidity.

Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually preserves information from the natural language side in the form of similar token…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …

A new tail-shape index based on Value at Risk and Expected Shortfall.

Reflected geometric Brownian motion models are not arbitrage-free.

We present a novel modulation level classification (MLC) method based on probability distribution distance functions. The proposed method uses modified Kuiper and Kolmogorov-Smirnov distances to achieve low computational complexity and outperforms the state of the art methods based on cumulants and goodness-of-fit test…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of…

A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…