Given two time series, A and B, sampled asynchronously at different times {t_A_i} and {t_B_j}, termed “ticks”, how can one best estimate the correlation coefficient ρbetween changes in A and B? We derive a natural, minimum-variance estimator that does not use any interpolation or binning, then deriv
The money market and the capital market of the Indian financial markets have a symbiotic relationship in the development of the Indian economy. The nature and the characteristics of the markets differ to a large extent as the money market ensures liquidity in the system through the monetary policy b
This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using
This paper studies the optimal liquidation of stocks in the presence of temporary and permanent price impacts, and we focus in the case of cryptocurrencies. We start by presenting analytical solutions to the problem with linear temporary impact, and linear and quadratic permanent impact. Then, using
We study the expected utility portfolio optimization problem in an incomplete financial market where the risky asset dynamics depend on stochastic factors and the portfolio allocation is constrained to lie within a given convex set. We employ fundamental duality results from real constrained optimiz
While ChatGPT’s linguistic capabilities have recently seen an explosion of interest in a variety of fields, its potential in finance, particularly investme
Selecting stock portfolios and assessing their relative volatility risk compared to the market as a whole, market indices, or other portfolios is of great importance to professional fund managers and individual investors alike. Our research uses the cross-sectional intrinsic entropy (CSIE) model to
Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is ava
The real options approach is now considered an effective alternative to the corporate DCF model for a feasibility study. The current paper offers a practical methodology employing binomial trees and real options techniques for evaluating investment projects. A general computation procedure is sugges
The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smal
We present a parsimonious neural network approach, which does not rely on dynamic programming techniques, to solve dynamic portfolio optimization problems subject to multiple investment constraints. The number of parameters of the (potentially deep) neural network remains independent of the number o
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the $q$-distribution family, which is characterized by
The paper is devoted to the study of the short rate equation of the form $$ dR(t)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=x\geq 0, \quad t>0, $$ with deterministic functions $F,G_1,…,G_d$ and independent Lévy processes of infinite variation $Z_1,…,Z_d$ with regularly varying Laplac
This paper explores Artificial Neural Network (ANN) as a model-free solution for a calibration algorithm of option pricing models. We construct ANNs to calibrate parameters for two well-known GARCH-type option pricing models: Duan’s GARCH and the classical tempered stable GARCH that significantly im
The concept of entropy is not uniquely relevant to the statistical mechanics but among others it can play pivotal role in the analysis of a time series, particularly the stock market data. In this area sudden events are especially interesting as they describe abrupt data changes which may have long-
We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset pri
Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any pre-specifications of retirement time, preferences, and mar
Quantitative markets are characterized by swift dynamics and abundant uncertainties, making the pursuit of profit-driven stock trading actions inherently challenging. Within this context, reinforcement learning (RL), which operates on a reward-centric mechanism for optimal control, has surfaced as a
This paper presents a novel hybrid approach for constricting probabilistic forecasts that combines both the Quantile Regression Averaging (QRA) method and the factor-based averaging scheme. The performance of the approach is evaluated on data sets from two European energy markets - the German EPEX S
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default ris