arXiv research

Study uses viscosity solutions to solve control problems involving measure-valued martingales.

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…

We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero et al. (2012) and Filipovic and Larsson (2016) is transferred to this infinite …

We solve a complex Bayesian control problem with novel methods.

Polynomial processes in Banach spaces via infinitesimal generator and ODEs.

Framework for energy markets using measure-valued processes.

Infinite dimensional measure-valued processes modeled as polynomial diffusions.

This work optimizes bid strategies for online auctions using measure-valued optimization.

Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.

The paper compares different risk measures for optimal portfolio strategies.

Hybrid model combines risk measures for better portfolio allocation.

Study on measure-valued CARMA processes in Banach spaces.

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…

New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.

We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional Lévy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation mart…

New algorithm selects robust martingale for optimal stopping problems.

A new diversification measure DQ derived from risk measures addresses limitations of existing indices.

Develops a martingale expansion for stochastic volatility models.

The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach to study curvature-dimension condition of smooth metric measure spac…

Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.

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

Active learning selects optimal measurement times for inferring continuous paths from sparse data.

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

In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a …

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

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.

The paper studies projections of asset prices under equivalent martingale measures.

Extends optimal transport to dynamic and martingale settings.

We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale $M$ are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form $σ(M_t,v_t),$ with $v_t$ being a stochastic volatility term.

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…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the m…

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…

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…

New method finds closest martingale to Brownian motion.

We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…

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…

Dynamic reinsurance aims to minimize surplus risk using martingale transport.

The stochastic exponential $Z_t=\exp\{M_t-M_0-(1/2) <M,M>_t\}$ of a continuous local martingale $M$ is itself a continuous local martingale. We give a necessary and sufficient condition for the process $Z$ to be a true martingale in the case where $M_t=\int_0^t b(Y_u)\,dW_u$ and $Y$ is a one-dimensional diffusion drive…

Efficiently computes robust option prices using multi-marginal martingale transport.

We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov …

We extend martingale transport results to weak martingale transport.

We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic processes generate uncorrelated, generally nonstationary increments. Generally,…

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 martingale \int H.dZ is defined as having Dimension k if H has rank k almost surely, almost all t. Dimension can be used as a geometric invariant to classify and study martingales. We also define general Brownian motions in higher dimensions.

Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.