arXiv research

A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.

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…

Characterizes measures preserving compound mixed renewal process properties.

In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete…

New insights into empirical Bayes and compound decision problems with improved regret bounds.

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model including the classical risk model and the Polya-Aeppli risk model as sp…

Study shows convergence rates for BSDEs approximated by compound Poisson processes.

Mack's estimator improves chain ladder prediction for large exposure insurance models.

A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can reproduce various stylized facts.

In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the compar…

Researchers calculated EVaR for various distributions using Lambert function.

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a station…

Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.

We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied bet…

Study parameter sensitivities in bond pricing models with jumps.

A method is developed to estimate the parameters of a Levy copula of a discretely observed bivariate compound Poisson process without knowledge of common shocks. The method is tested in a small sample simulation study. Also, the method is applied to a real data set and a goodness of fit test is developed. With the meth…

Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scala…

In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the ma…

Proposes a reverse stress testing framework for dynamic models.

We present a general framework, the coupled compound Poisson factorization (CCPF), to capture the missing-data mechanism in extremely sparse data sets by coupling a hierarchical Poisson factorization with an arbitrary data-generating model. We derive a stochastic variational inference algorithm for the resulting model …

Investigates RI strategies for life insurers with LRD mortality rates.

We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples th…

Study optimal reinsurance pricing under model uncertainty for multiple insurers.

Study short-maturity VIX and European option prices with jumps.

This work facilitates ensuring fairness of machine learning in the real world by decoupling fairness considerations in compound decisions. In particular, this work studies how fairness propagates through a compound decision-making processes, which we call a pipeline. Prior work in algorithmic fairness only focuses on f…

Study of bandit problem with Poisson decision times and Lévy processes.

In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of expected discoun…

We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modelled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, which in turn determines the demand. We compute the price of a…

New algorithm identifies best arm in rare event scenarios.

Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferen…

Count data are often used in recommender systems: they are widespread (song play counts, product purchases, clicks on web pages) and can reveal user preference without any explicit rating from the user. Such data are known to be sparse, over-dispersed and bursty, which makes their direct use in recommender systems chal…

Study shows subordinated Cramér-Lundberg model increases ruin probability.

We consider a two-dimensional optimal dividend problem in the context of two branches of an insurance company with compound Poisson surplus processes dividing claims and premia in some specified proportions. We solve the stochastic control problem of maximizing expected cumulative discounted dividend payments (among al…

We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow $N$ is given by a Poisson process, we give a full analysis of the prop…

Modeling dependent defaults with multivariate Cox processes.

A bandit problem with filtered Poisson process data.

The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.

This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …

In this paper we study a class of insurance products where the policy holder has the option to insure $k$ of its annual Operational Risk losses in a horizon of $T$ years. This involves a choice of $k$ out of $T$ years in which to apply the insurance policy coverage by making claims against losses in the given year. The…

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the stopping boundary and that it is $C^1$ everywhere (i.e. the smooth pasting conditio…

We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a conseq…

The Tweedie Compound Poisson-Gamma model is routinely used for modeling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping hierarchy in the data. An important application of Tweedie mixed models is pricing …

Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods are the Standard method of Maximum Entropy (SME), and the method of Maximum Entrop…

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differ…

The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company's interest to detect the change time as soon as possible in order to re-evaluate a new fair v…

Proposes RCL method to improve ATE estimation from observational data.

New method offsets DML's error-compounding issue and provides more stable causal parameter estimates.

A new method solves complex financial problems using deep learning.