Related papers: Spanning Multi-Asset Payoffs With ReLUs

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…

In this article, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We study how such options can be valued in terms of simple vanilla options in non-specified market models. We…

This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the…

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…

This paper aims to interpret the mechanism of feedforward ReLU networks by exploring their solutions for piecewise linear functions, through the deduction from basic rules. The constructed solution should be universal enough to explain some…

We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$.…

We study the problem of pricing variable annuities with a multi-layer expense strategy, under which the insurer charges fees from the policyholder's account only when the account value lies in some pre-specified disjoint intervals, where on…

In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…

In this paper we formulate a regression problem to predict realized volatility by using option price data and enhance VIX-styled volatility indices' predictability and liquidity. We test algorithms including regularized regression and…

We propose an efficient method of finding an optimal solution for a multi-item continuous review inventory model in which a bivariate Gaussian probability distribution represents a correlation between the demands of different items. By…

We reinterpret and propose a framework for pricing path-dependent financial derivatives by estimating the full distribution of payoffs using Distributional Reinforcement Learning (DistRL). Unlike traditional methods that focus on expected…

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…

We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…

We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive L\'evy) model. The first problem is a variant of the bail-out case where both dividend payments and…

Autonomous Market Makers (AMMs) rely on arbitrage to facilitate passive price updates. Liquidity fragmentation poses a complex challenge across different blockchain networks. This paper proposes FluxLayer, a solution to mitigate fragmented…

We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure. To do so, we propose a new…

This paper studies the problem of optimally allocating a cash injection into a financial system in distress. Given a one-period borrower-lender network in which all debts are due at the same time and have the same seniority, we address the…

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent.…

Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…