G/M/1 type structure in a regime-switching risk model with general claim sizes

2011 ◽  
Author(s):  
Jerim Kim ◽  
Bara Kim ◽  
Hwa-Sung Kim
Keyword(s):  
Regime Switching ◽  
Risk Model ◽  
Type Structure

scholarly journals Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

2005 ◽  
Vol 35 (02) ◽  
pp. 351-361 ◽  
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang
Keyword(s):  
Regime Switching ◽  
Joint Distribution ◽  
Risk Model ◽  
Insurance Risk ◽  
Additive Process ◽  
Deficit At Ruin ◽  
Markov Additive Process ◽  
The Deficit At Ruin ◽  
Markov Modulated ◽  
Markovian Regime Switching

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

scholarly journals Optimal Surplus-Dependent Reinsurance Under Regime-Switching in a Brownian Risk Model

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 73
Author(s):  
Julia Eisenberg ◽  
Lukas Fabrykowski ◽  
Maren Diane Schmeck
Keyword(s):  
Regime Switching ◽  
Risk Model ◽  
Numerical Approach ◽  
Hjb Equation ◽  
Recursive Procedure ◽  
Optimal Reinsurance ◽  
Surplus Process ◽  
Hamilton Jacobi Bellman ◽  
Capital Injections ◽  
A Company

In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuous-time Markov chain with two states. The presence of regime-switching substantially complicates the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first- and second-order derivatives. Via Ito’s formula, we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation.

EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk

2018 ◽  
Vol 3 (50) ◽  
pp. 01-25
Author(s):  
Marcin Chlebus
Keyword(s):  
At Risk ◽  
Regime Switching ◽  
Value At Risk ◽  
Risk Model ◽  
Empirical Distribution ◽  
Financial Time Series ◽  
Garch Models ◽  
Random Errors ◽  
A Value ◽  
Risk Forecasting

Abstract In the study, the two-step EWS-GARCH models to forecast Value-at-Risk is presented. The EWS-GARCH allows different distributions of returns or Value-at-Risk forecasting models to be used in Value-at-Risk forecasting depending on a forecasted state of the financial time series. In the study EWS-GARCH with GARCH(1,1) and GARCH(1,1), with the amendment to the empirical distribution of random errors as a Value-at-Risk model in a state of tranquillity and empirical tail, exponential or Pareto distributions used to forecast Value-at-Risk in a state of turbulence were considered. The evaluation of Value-at-Risk forecasts was based on the Value-at-Risk forecasts and the analysis of loss functions. Obtained results indicate that EWS-GARCH models may improve the quality of Value-at-Risk forecasts generated using the benchmark models. However, the choice of best assumptions for the EWS-GARCH model should depend on the goals of the Value-at-Risk forecasting model. The final selection may depend on an expected level of adequacy, conservatism and costs of the model.

scholarly journals On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenguang Yu
Keyword(s):  
Integral Equations ◽  
Penalty Function ◽  
Regime Switching ◽  
Risk Model ◽  
Expected Discounted Penalty Function ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Markovian Regime Switching ◽  
Expected Discounted Penalty ◽  
Markovian Regime

We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force process is also regulated by the Markovian regime-switching process. Applications of the integral equations are given to be the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. For exponential distribution, the explicit expressions for these quantities are obtained. Finally, a numerical example is also given to illustrate the effect of the related parameters on these quantities.

scholarly journals Discrete-Time Risk Models Based on Time Series for Count Random Variables

2010 ◽  
Vol 40 (1) ◽  
pp. 123-150 ◽  
Author(s):  
Hélène Cossette ◽  
Etienne Marceau ◽  
Véronique Maume-Deschamps
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Regime Switching ◽  
Risk Model ◽  
Dependence Structure ◽  
Serial Dependence ◽  
Bernoulli Process ◽  
Temporal Dependence ◽  
Risk Models ◽  
Numerical Examples

AbstractIn this paper, we consider various specifications of the general discrete-time risk model in which a serial dependence structure is introduced between the claim numbers for each period. We consider risk models based on compound distributions assuming several examples of discrete variate time series as specific temporal dependence structures: Poisson MA(1) process, Poisson AR(1) process, Markov Bernoulli process and Markov regime-switching process. In these models, we derive expressions for a function that allow us to find the Lundberg coefficient. Specific cases for which an explicit expression can be found for the Lundberg coefficient are also presented. Numerical examples are provided to illustrate different topics discussed in the paper.

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