Related papers: A martingale concept for non-monotone information …
In an incomplete market underpinned by the trinomial model, we consider two investors : an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded…
We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…
We present results on simulations of a stock market with heterogeneous, cumulative information setup. We find a non-monotonic behaviour of traders' returns as a function of their information level. Particularly, the average informed agents…
Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit…
We define dynamic treatment regimes and associated potential outcomes for data described by marked point processes (MPPs). These definitions motivate MPP analogues of the commonly used consistency, exchangeability, and positivity conditions…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has…
This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
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…
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
While information theory has been introduced to characterize the fundamental limitations of control and filtering for a few decades, the existing information-theoretic methods are indirect and cumbersome for analyzing the limitations of…
In this paper we study the pricing and hedging of nonreplicable contingent claims, such as long-term insurance contracts like variable annuities. Our approach is based on the benchmark-neutral pricing framework of Platen (2024), which…
We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation…
Our financial setting consists of a market model with two flows of information. The smallest flow F is the "public" flow of information which is available to all agents, while the larger flow G has additional information about the…