This paper states that for financial markets with continuous filtrations, the minimax local martingale measure defined by Frittelli is equivalent to the objective measure for nondecreasing but not strictly increasing utility functions if it exists, provided the dual utility function satisfies some boundedness assumptions for the relative risk aversion, and there exists an equivalent local marti...

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal martingale structure a general functional inhomogeneous singularly perturbed diffusion processes under second-order averaging, where is defined as logarithmic Radon–Nykodim derivative between laws original process and co...

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

The Spontaneous Symmetry breaking in Quantum Finance considers the martingale condition stock market as a vacuum state if we express financial equations Hamiltonian form. original analysis for this phenomena ignores completely kinetic terms neighborhood of minimal potential terms. This is correct most cases. However, when deal with Martingale condition, it comes out that can also behave and the...

In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P ), where μ and P are measures on C([0, T ];R). The underlying measure P is a weak solution to a martingale problem with continuous coefficients. Our representation is in the form of an integral with respect to its infinitesimal generator. This representation ...

We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).

The coherent risk framework is linked to martingale valuation by adding hedgeinvariance as a fifth axiom, motivated by the concept of consistent hedging. The resulting subclass, called coherent pre-hedge (CoPr) measures, is characterized by a martingale condition on the test set that underlies a coherent measure. It is also made explicit how consistent hedging, optimal as well as non-optimal, t...

Abstract The objective of this paper is to develop a duality between novel entropy martingale optimal transport (EMOT) problem and an associated optimisation problem. In EMOT, we follow the approach taken in (EOT) developed Liero et al. (Invent. Math. 211:969–1117, 2018), but add constraint, typical (MOT) theory, that infimum cost functional over probability measures. problem, functional, relat...

We consider the problem of modelling the term structure of bonds subject to default risk, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this requires the introduction of an additional term to the forward-rate approach by Heath, Jarro...

The original transport problem is to optimally move a pile of soil to an excavation. Mathematically, given two measures of equal mass, we look for an optimal map that takes one measure to the other one and also minimizes a given cost functional. Kantorovich relaxed this problem by considering a measure whose marginals agree with given two measures instead of a bijection. This generalization lin...