Related papers: Pathwise functional calculus and applications to c…
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, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing…
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…
We consider a strictly pathwise setting for Delta hedging exotic options, based on F\"ollmer's pathwise It\=o calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…
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 describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
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…
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…
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying…
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…
This paper presents a data-driven interpretable machine learning algorithm for semi-static hedging of Exchange Traded options, considering transaction costs with efficient run-time. Further, we provide empirical evidence on the performance…
We apply rough-path theory to study the discrete-time gamma-hedging strategy. We show that if a trader knows that the market price of a set of European options will be given by a diffusive pricing model, then the discrete-time gamma-hedging…
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static…
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…
Designing effective incentive mechanisms in mobile crowdsensing (MCS) networks is crucial for engaging distributed mobile users (workers) to contribute heterogeneous data for various applications (tasks). In this paper, we propose a novel…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…