Related papers: Building arbitrage-free implied volatility: Sinkho…
Consider a discrete-time infinite horizon financial market model in which the logarithm of the stock price is a time discretization of a stochastic differential equation. Under conditions different from those given in a previous paper of…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
In this paper, we derive a temporal arbitrage policy for storage via reinforcement learning. Real-time price arbitrage is an important source of revenue for storage units, but designing good strategies have proven to be difficult because of…
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP)…
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages:…
The purpose of this work is to explore the role that arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary…
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…
The Sinkhorn operator has recently experienced a surge of popularity in computer vision and related fields. One major reason is its ease of integration into deep learning frameworks. To allow for an efficient training of respective neural…
We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
There has been substantial progress recently in understanding toy problems of purely implicit signaling. These are problems where the source and the channel are implicit -- the message is generated endogenously by the system, and the plant…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.