Related papers: Superhedging Supermartingales
We present for the first time a supermartingale certificate for $\omega$-regular specifications. We leverage the Robbins & Siegmund convergence theorem to characterize supermartingale certificates for the almost-sure acceptance of Streett…
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…
We present a new deep primal-dual backward stochastic differential equation framework based on stopping time iteration to solve optimal stopping problems. A novel loss function is proposed to learn the conditional expectation, which…
We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.
We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or…
In this paper we provide a pricing-hedging duality for the model-independent superhedging price with respect to a prediction set $\Xi\subseteq C[0,T]$, where the superhedging property needs to hold pathwise, but only for paths lying in…
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices…
A supermartingale deflator (resp., local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp., local martingales). The supermartingale numeraire (resp., local martingale numeraire) is…
We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We study a variant of the martingale optimal transport problem in a multi-period setting to derive robust price bounds of a financial derivative. On top of marginal and martingale constraints, we introduce a time-homogeneity assumption,…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
Consider a financial market with nonnegative semimartingales which does not need to have a num\'{e}raire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities,…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous…
The goal of this paper is to define stochastic integrals and to solve stochastic differential equations for typical paths taking values in a possibly infinite dimensional separable Hilbert space without imposing any probabilistic structure.…
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the…