Related papers: Market viability and martingale measures under par…
A financial market is a system resulting from the complex interaction between participants in a closed economy. We propose a minimal microscopic model of the financial market economy based on the real economy's symmetry constraint and…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic…
We consider the problem of decomposing monetary risk in the presence of a fully traded market in {\it some} risks. We show that a mark-to-market approach to pricing leads to such a decomposition if the risk measure is time-consistent in the…
We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…
We introduce a new class of automated market maker (AMM), the \emph{partially active automated market maker} (PA-AMM). PA-AMM divides its reserves into two parts, the active and the passive parts, and uses only the active part for trading.…
Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his…
In an incomplete model, where under an appropriate num\'eraire, the stock price process is driven by a sigma-bounded semimartingale, we investigate the behavior of the expected utility maximization problem under small perturbations of the…
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\rm NA}_{1}(\mathcal{P})$ of no-arbitrage of the first…
We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
For any discrete-time $P$--local martingale $S$ there exists a probability measure $Q \sim P$ such that $S$ is a $Q$--martingale. A new proof for this result is provided. The core idea relies on an appropriate modification of an argument by…
We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite…
We consider a one-period market model composed by a risk-free asset and a risky asset with $n$ possible future values (namely, a $n$-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
We study a simple model of an asset market with informed and non-informed agents. In the absence of non-informed agents, the market becomes information efficient when the number of traders with different private information is large enough.…
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with…