THE EFFICIENT COMPUTATION AND THE SENSITIVITY ANALYSIS OF FINITE-TIME RUIN PROBABILITIES AND THE ESTIMATION OF RISK-BASED REGULATORY CAPITAL

2016 ◽  
Vol 46 (2) ◽  
pp. 431-467
Author(s):  
Mark S. Joshi ◽  
Dan Zhu
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Structural Parameters ◽  
Classical Model ◽  
Management Strategies ◽  
Rare Event ◽  
Insurance Companies ◽  
Ruin Probabilities ◽  
Efficient Computation ◽  
Regulatory Capital

AbstractSolvency regulations require financial institutions to hold initial capital so that ruin is a rare event. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically with less than 0.1% over a finite-time horizon. Estimating probabilities of rare events is challenging, since naive estimations via direct simulations of the surplus process is not feasible. In this paper, we present a stratified sampling algorithm for estimating finite-time ruin probabilities. We further introduce a sequence of measure changes to remove the pathwise discontinuities of the estimator, and compute unbiased first and second-order derivative estimates of the finite-time ruin probabilities with respect to both distributional and structural parameters. We then estimate the regulatory capital and its sensitivities. These estimates provide information to insurance companies for meeting prudential regulations as well as designing risk management strategies. Numerical examples are presented for the classical model, the Sparre Andersen model with interest and the periodic risk model with interest to demonstrate the speed and efficacy of our methodology.

On the De Vylder and Goovaerts Conjecture About Ruin for Equalized Claims

2014 ◽  
Vol 51 (03) ◽  
pp. 874-879 ◽  
Author(s):  
C. Y. Robert
Keyword(s):  
Open Problem ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Ruin Theory ◽  
Finite Time Ruin Probability

In ruin theory, the conjecture given in De Vylder and Goovaerts (2000) is an open problem about the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability evaluated in the associated model with equalized claim amounts. In this paper we consider a weaker version of the conjecture and show that the integrals of the ruin probabilities with respect to the initial risk reserve are uniformly comparable.

scholarly journals On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

2013 ◽  
Vol 50 (02) ◽  
pp. 309-322 ◽  
Author(s):  
Zechun Hu ◽  
Bin Jiang
Keyword(s):  
Interest Rate ◽  
Differential Equations ◽  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Two Dimensional ◽  
Asymptotic Expressions ◽  
Integral Differential Equations ◽  
Constant Interest Rate ◽  
Constant Interest

In this note we consider the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008) with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite-time ruin probabilities with respect to the joint ruin times T max(u 1,u 2) and T min(u 1,u 2) respectively.

scholarly journals On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

2013 ◽  
Vol 50 (2) ◽  
pp. 309-322 ◽  
Author(s):  
Zechun Hu ◽  
Bin Jiang
Keyword(s):  
Interest Rate ◽  
Differential Equations ◽  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Two Dimensional ◽  
Asymptotic Expressions ◽  
Integral Differential Equations ◽  
Constant Interest Rate ◽  
Constant Interest

In this note we consider the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008) with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite-time ruin probabilities with respect to the joint ruin times Tmax(u1,u2) and Tmin(u1,u2) respectively.

MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

2017 ◽  
Vol 47 (2) ◽  
pp. 417-435 ◽  
Author(s):  
Lourdes B. Afonso ◽  
Rui M. R. Cardoso ◽  
Alfredo D. Egídio dos Reis ◽  
Gracinda Rita Guerreiro
Keyword(s):  
Finite Time ◽  
Classical Model ◽  
Real Data ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Probability Of Ruin ◽  
Insurance Portfolio ◽  
Motor Insurance ◽  
Large Motor ◽  
The Impact

AbstractMotor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.

ASYMPTOTIC RUIN PROBABILITIES IN FINITE HORIZON WITH SUBEXPONENTIAL LOSSES AND ASSOCIATED DISCOUNT FACTORS

2005 ◽  
Vol 20 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Stochastic Processes ◽  
Discrete Time ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Finite Time Ruin Probability ◽  
Discount Factors ◽  
Subexponential Class

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

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