We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak convergence of the unique stationary measure to the invaria
Socially responsible investors build investment portfolios intending to incite social and environmental advancement alongside a financial return. Although Mean-Variance (MV) models successfully generate the highest possible return based on an investor’s risk tolerance, MV models do not make provisio
Stock market is often important as it represents the ownership claims on businesses. Without sufficient stocks, a company cannot perform well in finance. Predicting a stock market performance of a company is nearly hard because every time the prices of a company stock keeps changing and not constant
Designing dynamic portfolio insurance strategies under market conditions switching between two or more regimes is a challenging task in financial economics. Recently, a promising approach employing the value-at-risk (VaR) measure to assign weights to risky and riskless assets has been proposed in [“
Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this setting, the options used as hedging instruments also have to be pr
Credit risk in the China’s bond market has become increasingly evident, creating a progressively escalating risk of default for credit bond investors. Given the current incomplete and inaccurate bond information disclosure, timely tracking and forecasting the individual credit bond default risks hav
Ito’s Lemma implies that if $W$ is a Wiener process and $f$ is a twice continuously differentiable function, then the process $f(W)$ is the sum of a time integral and an Ito integral. The Ito integrand is not necessarily locally square integrable. This note provides a counterexample.
This short note illustrates the theoretical solution to a trader determining how to optimally swap her wealth into a target asset through on-chain operations. It offers the framework to solve optimal slippage parameters and optimal trade size.
We derive several sets of sufficient conditions for applicability of the new efficient numerical realization of the inverse $Z$-transform. For large $n$, the complexity of the new scheme is dozens of times smaller than the complexity of the trapezoid rule. As applications, pricing of European option
This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of results have been obtained for it. In particular, option pricing f
In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit n-circle as a concave
We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which
This study employs the annual unbalanced panel data of 42 listed banks in China from 2006 to 2021, adopts the non-radial and non-oriented super-efficiency Data envelopment analysis (Super-SBM-UND-VRS based DEA) model considering NPL as undesired output. Our results show that the profitability super-
Stock trend analysis has been an influential time-series prediction topic due to its lucrative and inherently chaotic nature. Many models looking to accurately predict the trend of stocks have been based on Recurrent Neural Networks (RNNs). However, due to the limitations of RNNs, such as gradient v
Since the inception of permissionless blockchains with Bitcoin in 2008, it became apparent that their most well-suited use case is related to making the financial system and its advantages available to everyone seamlessly without depending on any trusted intermediaries. Smart contracts across chains
Creating accurate predictions in the stock market has always been a significant challenge in finance. With the rise of machine learning as the next level in the forecasting area, this research paper compares four machine learning models and their accuracy in forecasting three well-known stocks trade
We consider a rational agent who at time $0$ enters into a financial contract for which the payout is determined by a quantum measurement at some time $T>0$. The state of the quantum system is given in the Heisenberg representation by a known density matrix $\hat p$. How much will the agent be willi
This article presents a simple but effective and efficient approach to improve the accuracy and stability of Least-Squares Monte Carlo. The key idea is to construct the ansatz of conditional expected continuation payoff using the finite-difference solution from one dimension, to be used in linear re
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such range-based risk measures are appropriate for risk management of re
Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogene