Olena Ragulina

National Taras Shevchenko University of Kyiv | Київський національний університет імені Тараса Шевченка · Department of Probability Theory, Statistics and Actuarial Mathematics

The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the E...

The authors wish to make the following corrections to this paper [1]:1 [...]

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we co...

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we co...

The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the E...

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we co...

This paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investigate conditions, under which it holds for a number of distributions of the premium and claim sizes. Ne...

We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct five- and three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for t...

The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed i...

The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed i...

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high...

Let {ξ1, ξ2,...} be a sequence of independent real-valued and possibly nonidentically distributed random variables. Suppose that η is a nonnegative, nondegenerate at 0 and integer-valued random variable, which is independent of {ξ1, ξ2,...}. In this paper, we consider conditions for {ξ1, ξ2,...} and η under which the distributions of the randomly s...

We propose a Monte Carlo simulation method to generate stress tests by VaR scenarios under Solvency II for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models. The approach is based on former work on partition-of-unity copulas, however with a direct scenario estimation of the joint d...

We consider the asymptotic behavior of the values P(S > x), E(S 1{S>x}), and E(S | S > x). Here S = θ1X1 + θ2X2 + · · · + θnXn is a randomly weighted sum of the basic random variables X1,X2, . . . , Xn, which follow some special dependence structure, and {θ1, θ2, . . . , θn} is a collection of nonnegative and arbitrarily dependent random weights; t...

We propose a new Monte Carlo simulation method to generate VaR scenarios for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models under Solvency II. The approach is based on former work on partition-of-unity copulas, however with a direct estimation of the joint density by product bet...

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas to continuous partition of copulas which were recently introduced in the literature, with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from hig...

The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie--Gumbel--Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We...

We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bon...

We present a constructive and self-contained approach to data driven general partition-of-unity copulas that were recently introduced in the literature. In particular, we consider Bernstein-, negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data.

In this chapter, we deal with generalizations of the classical risk model and the risk model with stochastic premiums where an insurance company invests all surplus in risk-free and risky assets proportionally. The price of the risky asset follows a jump process. We get upper and lower bounds for the infinite-horizon survival probability and invest...

In this chapter, we deal with a generalization of the classical risk model where an insurance company invests all surplus in a risk-free asset. We investigate the continuity and differentiability of the infinite- and finitehorizon survival probabilities in detail. Moreover, we derive integrodifferential equations for these functions and get bounds...

In this chapter, we deal with the classical risk model under the additional assumption that an insurance company applies a franchise and a liability limit. To be more precise, we consider three cases: the insurance company establishes a franchise only, a liability limit only and both a franchise and a liability limit. Assuming that claim sizes are...

In this chapter, we consider a generalization of the classical risk model where a premium intensity depends on a current surplus of an insurance company. The surplus is invested in one risk-free and a few risky assets. In addition, borrowing is also possible. The prices of the risky assets follow geometric Brownian motions, which are not necessaril...

In this chapter, we formulate some basic results concerning ruin probabilities in the classical risk model and the risk model with stochastic premiums.

In this chapter, we consider a generalization of the classical risk model where a premium intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion, but an insurance company stops its investment activity when the price of the risky asset goes do...

In this chapter, we consider a generalization of the risk model with stochastic premiums where an insurance company invests all surplus in a risk-free asset. We investigate the continuity and differentiability of the infinite- and finite-horizon survival probabilities and compare these results with those in the case of zero interest rate. Furthermo...

In this chapter, we consider a generalization of the classical risk model where premium intensity depends on a current surplus of an insurance company. All surplus is invested in one risky asset, the price of which follows a geometric Brownian motion. Our main aim is to show that if the premium intensity grows rapidly with increasing surplus, then...

In this chapter, we consider the classical risk model where an insurance company is able to adjust a franchise amount continuously. The problem of optimal control by the franchise amount is solved from the viewpoint of survival probability maximization. We derive the Hamilton–Jacobi–Bellman equation for the optimal survival probability and prove th...

Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-hor...

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an upper exponential bound and construct an analogue to the De Vylder approximation for the ruin probability. We co...

We consider the classical risk model when an insurance company has the opportunity to adjust franchise amount continuously. The problem of optimal control by franchise amount is solved from viewpoint of survival probability maximization. We derive the Hamilton–Jacobi–Bellman equation for the optimal survival probability and prove the existence of a...

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus proce...