Related papers: Hedging with Small Uncertainty Aversion
Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…
It's regarded as an axiom that a good model is one that compromises between bias and variance. The bias is measured in training cost, while the variance of a (say, regression) model is measure by the cost associated with a validation set.…
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the…
An investor with constant relative risk aversion and an infinite planning horizon trades a risky and a safe asset with constant investment opportunities, in the presence of small transaction costs and a binding exogenous portfolio…
We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…
Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…
In this paper, we explore the pricing and hedging strategies for an innovative insurance product called the equity protection swap(EPS). Notably, we focus on the application of EPSs involving cross-currency reference portfolios, reflecting…
Hedging strategies in bond markets are computed by martingale representation and the Clark-Ocone formula under the choice of a suitable of numeraire, in a model driven by the dynamics of bond prices. Applications are given to the hedging of…
We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing,…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…
The adaptation and use of Machine Learning (ML) in our daily lives has led to concerns in lack of transparency, privacy, reliability, among others. As a result, we are seeing research in niche areas such as interpretability, causality, bias…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
Providing a measure of market risk is an important issue for investors and financial institutions. However, the existing models for this purpose are per definition symmetric. The current paper introduces an asymmetric capital asset pricing…
This paper investigates the pricing and hedging of variance swaps under a $3/2$ volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the…
This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…
We give elementary examples within a framework for studying decisions under uncertainty where probabilities are only roughly known. The framework, in gambling terms, is that the size of a bet is proportional to the gambler's perceived…
We introduce a pricing kernel with time-varying volatility risk aversion to explain observed time variations in the shape of the pricing kernel. When combined with the Heston-Nandi GARCH model, this framework yields a tractable option…