Related papers: Pathwise functional calculus and applications to c…
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…
Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is…
This paper proposes a simple technical approach for the analytical derivation of Point-in-Time PD (probability of default) forecasts, with minimal data requirements. The inputs required are the current and future Through-the-Cycle PDs of…
An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility…
This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model and a Hawkes process with a power kernel to capture the path dependence of the…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
Delta hedging, which plays a crucial r\^ole in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of…
In most real scenarios the construction of a risk-neutral portfolio must be performed in discrete time and with transaction costs. Two human imposed constraints are the risk-aversion and the profit maximization, which together define a…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
We derive a functional change of variable formula for {\it non-anticipative} functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for…
We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a…
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…
This paper proposes a portfolio construction framework designed to remain robust under estimation error, non-stationarity, and realistic trading constraints. The methodology combines dynamic asset eligibility, deterministic rebalancing, and…