Related papers: A dynamic version of the super-replication theorem…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…
We prove a continued fraction expansion for the reciprocal of a certain $q$-series. All the specialists in the world are asked whether it is new or not.
We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as…
We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal…
We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several…
In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of…
A well known result in stochastic analysis reads as follows: for an $\mathbb{R}$-valued super-martingale $X = (X_t)_{0\leq t \leq T}$ such that the terminal value $X_T$ is non-negative, we have that the entire process $X$ is non-negative.…
We consider a multivariate financial market with transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in…
We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known…
This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows…
We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
This is a supplement to the paper "Liquidity based modeling of asset price bubbles via random matching". The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D…
In this paper, we introduce a novel rule for synthesis of reactive systems, applicable to systems made of n components which have each their own objectives. It is based on the notion of admissible strategies. We compare our novel rule with…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…
We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the…
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the…