Related papers: A Direct Solution Method for Pricing Options in Re…
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…
We address an optimal stopping problem over the set of Bermudan-type strategies $\Theta$ (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear…
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can…
Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper [5] gives a closed form approximation formula…
A monopoly platform sells either a risky product (with unknown utility) or a safe product (with known utility) to agents who sequentially arrive and learn the utility of the risky product by the reporting of previous agents. It is costly…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for…
The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…
We propose two parametric approaches to evaluate swing contracts with firm constraints. Our objective is to define approximations for the optimal control, which represents the amounts of energy purchased throughout the contract. The first…
We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed…
Dynamic pricing schemes were introduced as an alternative to posted-price mechanisms. In contrast to static models, the dynamic setting allows to update the prices between buyer-arrivals based on the remaining sets of items and buyers, and…
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to…
This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…
Time or money? That is a question! In this paper, we consider this dilemma in the pricing regime, in which we try to find the optimal pricing scheme for identical items with heterogenous time-sensitive buyers. We characterize the…
In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
Option pricing models, essential in financial mathematics and risk management, have been extensively studied and recently advanced by AI methodologies. However, American option pricing remains challenging due to the complexity of…
An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its…