Related papers: Numerical analysis on locally risk-minimizing stra…

We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for…

We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck…

We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast…

The Barndorff-Nielsen and Shephard model is a representative jump-type stochastic volatility model. Still, no method exists to compute option prices numerically for the non-martingale case with infinite active jumps. We develop two…

This paper aims to develop a supervised deep-learning scheme to compute call option prices for the Barndorff-Nielsen and Shephard model with a non-martingale asset price process having infinite active jumps. In our deep learning scheme,…

We explore local risk-minimization, a quadratic hedging method for incomplete markets, in exponential additive models. The objectives are to derive explicit mathematical expressions and to conduct numerical experiments. While local…

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of…

In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…

In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent iterative method, is proposed and analyzed to find multiple…

In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are…

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie…

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC)…

In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the…

We compute and discuss the Esscher martingale transform for exponential processes, the Esscher martingale transform for linear processes, the minimal martingale measure, the class of structure preserving martingale measures, and the minimum…

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal…

Latent Space (LS) network models project the nodes of a network on a $d$-dimensional latent space to achieve dimensionality reduction of the network while preserving its relevant features. Inference is often carried out within a Markov…

In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of…

A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…