Related papers: A model-free approach to continuous-time finance
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
We present a non-probabilistic, path-by-path framework for studying path-dependent (i.e., where weight is a functional of time and historical time-series), long-only portfolio allocation in continuous-time based on [Chiu & Cont '23], where…
In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via…
We provide a simple and straightforward approach to a continuous-time version of Cover's universal portfolio strategies within the model-free context of F\"ollmer's pathwise It\^o calculus. We establish the existence of the universal…
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order…
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on F{\"o}llmer…
The main purpose of this work is the derivation of a functional partial differential equation (FPDE) for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial…
We construct a new topology on the space of stopped paths and introduce a calculus for causal functionals on generic domains of this space. We propose a generic approach to pathwise integration without any assumption on the variation index…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…
This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain…
The paper develops no arbitrage results for trajectory based models by imposing general constraints on the trading portfolios. The main condition imposed, in order to avoid arbitrage opportunities, is a local continuity requirement on the…
We introduce a performance-driven framework for constructing strictly causal forward-oriented observables in strongly non-stationary time series. The method combines a robustly normalized composite of heterogeneous indicators with a…
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that…
We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback…
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. In contrast with previous…
Functional It^o calculus is based on an extension of the classical It^o calculus to functionals depending on the entire past evolution of the underlying paths and not only on its current value. The calculus builds on Follmer's…
We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at…