Related papers: Robust martingale selection problem and its connec…
We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary…
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations,…
We study portfolio selection in a model with both temporary and transient price impact introduced by Garleanu and Pedersen (2016). In the large-liquidity limit where both frictions are small, we derive explicit formulas for the…
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
We introduce the concept of no-arbitrage in a credit risk market under ambiguity considering an intensity-based framework. We assume the default intensity is not exactly known but lies between an upper and lower bound. By means of the…
We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising…
We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections…
We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected…
We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding market weights. These models substantially extend volatility…