The paper develops methods to price derivatives in a time-varying, age-dependent market.
problem Pricing derivatives in a market with time-inhomogeneous volatility and age-dependent processes.
method Geometric Brownian motion model with time-varying volatility and age-dependent semi-Markov processes. Solves a non-local PDE and integral equation.
result Explicit expressions for derivative prices and hedging strategies are derived.
Improved sex and age-specific model for Parkinson's diagnosis.
problem Accurate diagnosis of Parkinson's disease for better patient care.
method Sex-specific and age-dependent handwriting classification model.
result Significantly improved accuracy (83.75% for females, 79.55% for older age group) compared to generalized model.
The paper analyzes optimal retirement timing considering age-dependent mortality risk.
problem Optimal retirement timing under age-dependent mortality risk.
method Formulated as a stochastic control and optimal stopping problem, transformed into a finite time horizon, three-dimensional degenerate optimal stopping problem.
result Existence of an optimal retirement boundary, characterized as a unique solution to a nonlinear integral equation.
This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a c…
Optimizes pension fund strategies considering age-dependent risk preferences.
problem Maximizing utility of future consumption and wealth in DC pension plans.
method Solves optimal consumption and investment policies using Black-Scholes framework and HARA utility functions.
result Only extended model with time-varying preference parameters provides adequate fit for real-life data.
Optimal annuitization strategy depends on age, labor income, and mortality risk.
problem Maximizing utility from consumption and labor income under age-dependent mortality.
method Dynamic programming approach to derive closed-form solutions.
result Post-retirement labor income acts as a substitute for annuitization.
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on the finite time horizon. We study the problem by using a …
Unified framework explains retirement and annuitization decisions under age-dependent mortality.
problem Complexity of annuitization decisions due to longevity risk and labor force participation.
method Stochastic control and optimal stopping framework with habit formation and endogenous labor supply.
result Rich sequence of retirement dynamics, including defensive and aggressive labor supply phases.
Optimizes pension mix of PAYGO, EET, and individual savings.
problem Balancing PAYGO, EET, and individual savings in funded pension schemes.
method Solves a Nash equilibrium between pension participants and government, considering age-dependent preferences and optimal asset allocation.
result Identifies critical ages and optimal contribution rates for maximizing overall utility.
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide downside protection. A tractable stochastic mortality model with age dependent …
Paper proposes a method to model health outcomes using varying-coefficients and KNN-based LASSO.
problem Modeling health outcomes like BMI and cholesterol levels with varying age effects.
method Varying-coefficients regional quantile regression via KNN fused LASSO, with ADMM algorithm.
result Efficacy in capturing complex age-dependent associations between health outcomes and risk factors.
The paper optimizes pension policies with guarantees and sustainability constraints.
problem Designing optimal pension policies with guarantees and sustainability constraints.
method Dynamic utility model, stochastic domain, overlapping generations, time-consistent decision criterion.
result Optimal investment/pension policy computed for a general framework.
Model trains agents to optimize saving and investment strategies for diverse retirement needs.
problem Optimal saving and investment strategies for individuals in varied employment and income profiles.
method Deep reinforcement learning to train intelligent agents with heterogeneous profiles.
result Flexible methodology estimates lifetime consumption and investment choices for different profiles.
The evolution of personal income distribution (PID) in four countries: Canada, New Zealand, the UK, and the USA follows a unique trajectory. We have revealed precise match in the shape of two age-dependent features of the PID: mean income and the portion of people with the highest incomes (2 to 5% of the working age po…
Study on Bitcoin transaction flows and holding times, revealing multifractal and power-law distributions.
problem Characterizing the temporal behavior and variability of Bitcoin transactions and holding times.
method Analysis of Bitcoin transaction data, including holding-time distributions, multiscaling, and multifractality.
result Found multifractal and power-law distributions in Bitcoin transaction flows and holding times, with significant variations in holding times.
Predicts gender and age from mobile phone data for marketing.
problem Enhance marketing offers by predicting customer demographics.
method Machine learning algorithms applied to CDRs, CRM, and billing info.
result 85.6% accuracy in gender prediction, 65.5% in age prediction.
Develops algorithms to optimize machine replacement schedules using operational data.
problem Optimizing machine replacement intervals when the lifetime distribution is unknown.
method Formulates as a stochastic multi-armed bandit problem and proposes Hoeffding- and Bernstein-based algorithms.
result Achieves optimal or near-optimal replacement intervals with minimal regret.
Develops a method to analyze SARS-CoV-2 viral load vs. age, finding a significant increase.
problem Determining if SARS-CoV-2 viral load depends on patient age.
method Flexible, non-parametric, hierarchical, Bayesian, causal model.
result Statistically significant increase in viral load with age, but only for one dataset.
A declining CVaR glidepath framework for TDF design with Chilean pension system application
problem Designing Target-Date Funds around an explicit return objective while controlling risk
method Propose a framework for designing TDFs with a declining CVaR constraint
result Key feature: conservative evaluation of each glidepath
Introduces a new class of hybrid processes combining Markov chains and Hawkes processes.
problem Characterize and ensure existence and uniqueness of complex hybrid marked point processes.
method Defines hybrid marked point processes implicitly via intensity and state process interactions, proving existence and uniqueness under general assumptions.
result Proves existence and uniqueness of hybrid marked point processes, extending existing results.
This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson proc…
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
The study examines Hawkes processes and their long-term behavior.
problem Understanding the long-term behavior of Hawkes processes.
method Proving functional limit theorems under various conditions on the dispersion of child events.
result Functional limit theorems hold for Hawkes processes with different levels of child event dispersion.
Paper discovers process models from online event streams.
problem Discovering process models from continuous event streams.
method Generic architecture for process discovery in event streams.
result The proposed architecture enables process discovery from event streams.
Elliptical processes generalize Gaussian and Student-t models with fat tails and computational efficiency.
problem Need for models with fat tails and computational tractability.
method Represent elliptical distributions as continuous mixtures of Gaussian distributions, derive closed-form expressions for marginal and conditional distributions.
result Elliptical processes offer advantages in robust regression compared to Gaussian processes.
Directly proves CRP from stick-breaking process without measure theory.
problem Indirect proof of CRP from stick-breaking process is complex.
method Direct proof using stick-breaking process to CRP, avoiding measure theory.
result Direct proof connects stick-breaking process to CRP.
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
SNP extends Neural Processes to handle temporal dependencies in sequences.
problem Handling temporal dependencies in sequences of stochastic processes.
method Integrates a temporal state-transition model into Neural Processes.
result First 4D model capable of dynamic 3D scene modeling.
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
Efficient methods for Lévy models using SINH-regular processes.
problem Efficient numerical methods for evaluating Lévy models.
method Defining SL-processes and sSL-processes, deriving properties of characteristic exponent, and showing all popular Lévy processes can be subordinated to Brownian motion.
result All crucial properties of characteristic exponent are consequences of a specific representation, and all popular Lévy processes are SL- or sSL-subordinated Brownian motion.
GRM uses graph neural networks to score process activity relevance.
problem Improving business processes with performance measures.
method Graph Relevance Miner (GRM) based on graph neural networks.
result Quantitatively evaluated relevance scores with four datasets.
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
Paper proposes a new method for online process discovery.
problem Online process discovery requires limited memory.
method Mapped online process discovery to cache memory management and applied cache replacement policies.
result Implemented and evaluated a new approach for online process discovery.
Student's-T processes improve on Gaussian processes by handling outliers and variance more flexibly.
problem Outliers and variance limitations in Gaussian processes.
method Generalization of Gaussian processes using Student's-T distribution, with new kernel function and update rule.
result Student's-T processes provide better performance in Bayesian optimization, especially with outliers.
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
Proposes a new BSP-Tree process for flexible space partition modeling.
problem Limited modelling flexibility of axis-aligned partitions in Mondrian process.
method Introduces a self-consistent Binary Space Partitioning (BSP)-Tree process with oblique cuts.
result Clear inferential improvements over standard Mondrian process and related methods.
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
Recurrent neural networks improve process instance classification.
problem Classifying ongoing process instances based on activities.
method Applied recurrent neural networks, specifically GRU, to classify business process instances.
result GRU outperforms LSTM in training time with similar accuracy.
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give t…
Deep learning predicts business process events with high precision.
problem Predicting next events in business processes.
method Recurrent neural networks applied to deep learning.
result Deep learning surpasses state-of-the-art in prediction precision.
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from cond…
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
Unified approach for drawdown and drawup of Markov processes.
problem Study of drawdown and drawup in time-homogeneous Markov processes.
method Short-time pathwise analysis, integral equation solution.
result Unified approach to study various drawdown quantities.
New process from fractional BM and OU process yields simpler variance.
problem Simpler model for autocovariance structure.
method Construct new process using fractional BM and OU process, analyze increments.
result Variance of new process easier to compute than FARIMA.
Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.