Related papers: A model-free approach to continuous-time finance
In an incomplete market driven by time-changed L\'evy noises we consider the problem of hedging a financial position coupled with the underlying risk of model uncertainty. Then we study hedging under worst-case-scenario. The proposed…
We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
We study the problem of estimating the value function of discrete-time switched systems under arbitrary switching. Unlike the switched LQR problem, where both inputs and mode sequences are optimized, we consider the case where switching is…
Stochastic integrals are defined with respect to a collection $P = (P_i; \, i \in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\mathbb{R}^I$ where $P$ takes values. The integrals are…
This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $\alpha \in (0, 1)$ and a Bolza cost functional. The differential game is associated to the…
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…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the…
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price…
Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are…
Classical portfolio models degrade under structural breaks, whereas flexible machine-learning allocation methods often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…