Related papers: Parallel-in-Time Iterative Methods for Pricing Ame…
In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient constraint and a partial integro-differential operator whose L\'evy measure…
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…
In this paper, we study option pricing under Vasicek Model by a Hamiltonian approach. Since the interest rate changes with time, we split the time to maturity into infinite steps, and the matrix element during each step could be calculated…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the…
It is well known that the Black-Scholes-Merton model suffers from several deficiencies. Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in this classical model. Unfortunately, the…
In reinforcement learning (RL), the long-term behavior of decision-making policies is evaluated based on their average returns. Distributional RL has emerged, presenting techniques for learning return distributions, which provide additional…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European…
We discuss time-optimal control problems for two setups involving globally driven Rydberg atoms in the blockade limit by deriving the associated Hamilton-Jacobi-Bellman equations. From these equations, we extract the globally optimal…
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity…
In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…
The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems motivated by finance. Impulses, which are controlled jumps in a…