Related papers: A model-free approach to continuous-time finance
We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of $p$-th variation along a sequence of time…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
Constant Product Market Makers use fees that are typically fixed proportions of trade size. When these fees are automatically reinvested into the pool, as in Uniswap~V2 and some designs of Uniswap V4, the final state after a trade can…
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard…
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
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…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
In this work we present the fundamental ideas of inference over paths, and show how this formalism implies the continuity equation, which is central for the derivation of the main partial differential equations that constitute…
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
We consider an incomplete market with a nontradable stochastic factor and a continuous time investment problem with an optimality criterion based on monotone mean-variance preferences. We formulate it as a stochastic differential game…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the…
We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the…